Total Mean Curvature And Submanifolds Of Finite Type

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Total Mean Curvature and Submanifolds of Finite Type

Author : Bang-yen Chen
Publisher : World Scientific Publishing Company
ISBN 13 : 9789971966027
Total Pages : 368 pages
Book Rating : 4.9/5 (66 download)

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Book Synopsis Total Mean Curvature and Submanifolds of Finite Type by : Bang-yen Chen

Download or read book Total Mean Curvature and Submanifolds of Finite Type written by Bang-yen Chen and published by World Scientific Publishing Company. This book was released on 1984 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to introduce the reader to two interesting topics in geometry which have developed over the last fifteen years, namely, total mean curvature and submanifolds of finite type. The theory of total mean curvature is the study of the integral of the n-th power of the mean curvature of a compact n-dimensional submanifold in a Euclidean m-space and its applications to other branches of mathematics. The relation of total mean curvature to analysis, geometry and topology are discussed in detail. Motivated from these studies, the author introduces and studies submanifolds of finite type in the last chapter. Some applications of such submanifolds are also given. This book is self-contained. The author hopes that the reader will be encouraged to pursue his studies beyond the confines of the present book.

Total Mean Curvature And Submanifolds Of Finite Type (2nd Edition)

Author : Bang-yen Chen
Publisher : World Scientific Publishing Company
ISBN 13 : 9814616710
Total Pages : 486 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Total Mean Curvature And Submanifolds Of Finite Type (2nd Edition) by : Bang-yen Chen

Download or read book Total Mean Curvature And Submanifolds Of Finite Type (2nd Edition) written by Bang-yen Chen and published by World Scientific Publishing Company. This book was released on 2014-10-29 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This unique and expanded second edition comprises a comprehensive account of the latest updates and new results that cover total mean curvature and submanifolds of finite type. The longstanding biharmonic conjecture of the author's and the generalized biharmonic conjectures are also presented in details. This book will be of use to graduate students and researchers in the field of geometry.

Pseudo-riemannian Geometry, Delta-invariants And Applications

Author : Bang-yen Chen
Publisher : World Scientific
ISBN 13 : 9814462489
Total Pages : 510 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Pseudo-riemannian Geometry, Delta-invariants And Applications by : Bang-yen Chen

Download or read book Pseudo-riemannian Geometry, Delta-invariants And Applications written by Bang-yen Chen and published by World Scientific. This book was released on 2011-03-23 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included.The second part of this book is on δ-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as δ-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between δ-invariants and the main extrinsic invariants. Since then many new results concerning these δ-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades.

Differential Geometry: Riemannian Geometry

Author : Robert Everist Greene
Publisher : American Mathematical Soc.
ISBN 13 : 0821814966
Total Pages : 735 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differential Geometry: Riemannian Geometry by : Robert Everist Greene

Download or read book Differential Geometry: Riemannian Geometry written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 3 begins with an overview by R.E. Greene of some recent trends in Riemannia

Geometry And Topology Of Submanifolds Iv - Proceedings Of The Conference On Differential Geometry And Vision

Author : Franki Dillen
Publisher : World Scientific
ISBN 13 : 9814554626
Total Pages : 298 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Geometry And Topology Of Submanifolds Iv - Proceedings Of The Conference On Differential Geometry And Vision by : Franki Dillen

Download or read book Geometry And Topology Of Submanifolds Iv - Proceedings Of The Conference On Differential Geometry And Vision written by Franki Dillen and published by World Scientific. This book was released on 1992-07-17 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings on pure and applied differential geometry, discusses several subjects in submanifold theory, such as the Willmore problem, minimal surfaces, submanifolds of finite type, affine differential geometry, indefinite Riemannian geometry, and applications of differential geometry in human and artificial vision.

Geometry And Topology Of Submanifolds, Iii: Proceedings Of The Leeds Differential Geometry Workshop 1990

Author : Alan West
Publisher : World Scientific
ISBN 13 : 9814611344
Total Pages : 336 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Geometry And Topology Of Submanifolds, Iii: Proceedings Of The Leeds Differential Geometry Workshop 1990 by : Alan West

Download or read book Geometry And Topology Of Submanifolds, Iii: Proceedings Of The Leeds Differential Geometry Workshop 1990 written by Alan West and published by World Scientific. This book was released on 1991-04-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This workshop collected together works by experts working in various aspects of the differential geometry of submanifold and discussed recent advances and unsolved problems. Two important linking lectures were on the work done by Thorbergsson and others on classifying isoparametric submanifolds of Euclidean spaces and the generalisation of these to Hilbert spaces due to Terng and others. Isoparametric submanifolds provides examples of minimal, taut submanifolds, of harmonic maps and submanifolds with parallel second fundamental form-all topics discussed at this workshop. There were also lectures on the rapidly developing topic of the affine geometry of hypersurfaces and on applications. Amomg the applications discussed are new methods for using PDE's for generating surfaces with special shapes for use in engineering design.

Differential Geometry

Author : Ion Mihai
Publisher : MDPI
ISBN 13 : 303921800X
Total Pages : 166 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Differential Geometry by : Ion Mihai

Download or read book Differential Geometry written by Ion Mihai and published by MDPI. This book was released on 2019-11-21 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and trans-Sasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both well-known geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.

Handbook of Differential Geometry, Volume 1

Author : F.J.E. Dillen
Publisher : Elsevier
ISBN 13 : 0080532837
Total Pages : 1067 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Differential Geometry, Volume 1 by : F.J.E. Dillen

Download or read book Handbook of Differential Geometry, Volume 1 written by F.J.E. Dillen and published by Elsevier. This book was released on 1999-12-16 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry

Author : Ye-lin Ou
Publisher : World Scientific
ISBN 13 : 9811212392
Total Pages : 541 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry by : Ye-lin Ou

Download or read book Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry written by Ye-lin Ou and published by World Scientific. This book was released on 2020-04-04 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.

Recent Advances in the Geometry of Submanifolds

Author : Bogdan D. Suceavă
Publisher : American Mathematical Soc.
ISBN 13 : 1470422980
Total Pages : 224 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Advances in the Geometry of Submanifolds by : Bogdan D. Suceavă

Download or read book Recent Advances in the Geometry of Submanifolds written by Bogdan D. Suceavă and published by American Mathematical Soc.. This book was released on 2016-09-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, held from October 25–26, 2014, at San Francisco State University, San Francisco, CA, and the AMS Special Session on Recent Advances in the Geometry of Submanifolds: Dedicated to the Memory of Franki Dillen (1963–2013), held from March 14–15, 2015, at Michigan State University, East Lansing, Ml. The focus of the volume is on recent studies of submanifolds of Riemannian, semi-Riemannian, Kaehlerian and contact manifolds. Some of these use techniques in classical differential geometry, while others use methods from ordinary differential equations, geometric analysis, or geometric PDEs. By brainstorming on the fundamental problems and exploring a large variety of questions studied in submanifold geometry, the editors hope to provide mathematicians with a working tool, not just a collection of individual contributions. This volume is dedicated to the memory of Franki Dillen, whose work in submanifold theory attracted the attention of and inspired many geometers.

Differential Geometry and Global Analysis

Author : Bang-Yen Chen
Publisher : American Mathematical Society
ISBN 13 : 1470460157
Total Pages : 242 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Differential Geometry and Global Analysis by : Bang-Yen Chen

Download or read book Differential Geometry and Global Analysis written by Bang-Yen Chen and published by American Mathematical Society. This book was released on 2022-04-07 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930–2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while recalling historical results, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the $(M_{+}, M_{-})$ method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.

Advances in Algebra Analysis and Topology

Author : Sandeep Singh
Publisher : CRC Press
ISBN 13 : 104022475X
Total Pages : 141 pages
Book Rating : 4.0/5 (42 download)

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Book Synopsis Advances in Algebra Analysis and Topology by : Sandeep Singh

Download or read book Advances in Algebra Analysis and Topology written by Sandeep Singh and published by CRC Press. This book was released on 2024-12-19 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents cutting-edge research, advanced techniques, and practical applications of Algebra Analysis and Topology. It offers in-depth insights, theoretical developments, and practical applications, showcasing the richness and interdisciplinary nature of algebra, analysis, and topology. The book fosters a deeper understanding of the fundamental principles while also highlighting the latest advancements and emerging trends in these disciplines. Readers are encouraged to apply the theoretical concepts and techniques to solve mathematical problems, engaging with the book's problem-solving approach. By combining theoretical foundations, practical applications, and interdisciplinary perspectives, this book aims to inspire new avenues of research and contribute to the ongoing development of these dynamic fields. • Provides a comprehensive and accessible resource that covers a broad range of topics in algebra, analysis, and topology, understanding of the interconnections between these mathematical fields • Encompasses both classical topics and cutting-edge research areas within algebra, analysis, and topology • Covers foundational concepts, advanced theories, and their applications in diverse fields such as physics, computer science, engineering, and economics • Offers sophisticated tools and methodologies to tackle complex problems and deepen the understanding of these disciplines • Explores how algebra, analysis, and topology intersect with other fields of mathematics and how their concepts and techniques can be applied in related disciplines It serves as a valuable reference for graduate students, researchers, and mathematicians seeking to deepen their knowledge and engage with the latest advancements in these fundamental branches of mathematics.

Geometry And Topology Of Submanifolds Viii

Author : Ignace Van De Woestyne
Publisher : World Scientific
ISBN 13 : 9814547514
Total Pages : 426 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Geometry And Topology Of Submanifolds Viii by : Ignace Van De Woestyne

Download or read book Geometry And Topology Of Submanifolds Viii written by Ignace Van De Woestyne and published by World Scientific. This book was released on 1996-10-25 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings consists of papers presented at the international meeting of Differential Geometry and Computer Vision held in Norway and of international meetings on Pure and Applied Differential Geometry held in Belgium. This volume is dedicated to Prof Dr Tom Willmore for his contribution to the development of the domain of differential geometry. Furthermore, it contains a survey on recent developments on affine differential geometry, including a list of publications and a problem list.

Geometry And Topology Of Submanifolds Vi - Pure And Applied Differential Geometry And The Theory Of Submanifolds

Author : Franki Dillen
Publisher : World Scientific
ISBN 13 : 9814550655
Total Pages : 326 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Geometry And Topology Of Submanifolds Vi - Pure And Applied Differential Geometry And The Theory Of Submanifolds by : Franki Dillen

Download or read book Geometry And Topology Of Submanifolds Vi - Pure And Applied Differential Geometry And The Theory Of Submanifolds written by Franki Dillen and published by World Scientific. This book was released on 1994-09-30 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics covered are pure differential geometry, especially submanifolds and affine differential geometry, and applications of geometry to human vision, robotics, and gastro-entrology.

Geometry And Topology Of Submanifolds Ii

Author : Boyom M
Publisher : #N/A
ISBN 13 : 9814611522
Total Pages : 424 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Geometry And Topology Of Submanifolds Ii by : Boyom M

Download or read book Geometry And Topology Of Submanifolds Ii written by Boyom M and published by #N/A. This book was released on 1990-05-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods

Author : Hajime Urakawa
Publisher : World Scientific
ISBN 13 : 9813236418
Total Pages : 349 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods by : Hajime Urakawa

Download or read book Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods written by Hajime Urakawa and published by World Scientific. This book was released on 2018-12-06 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers. In the reviewer’s opinion, this excellent monograph will be a basic reference for graduate students and researchers working in the field of differential geometry of variational methods.'zbMATHThe author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and also fundamental materials of differential geometry.

The Problem Of Plateau: A Tribute To Jesse Douglas And Tibor Rado

Author : Themistocles M Rassias
Publisher : World Scientific
ISBN 13 : 9814506400
Total Pages : 350 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis The Problem Of Plateau: A Tribute To Jesse Douglas And Tibor Rado by : Themistocles M Rassias

Download or read book The Problem Of Plateau: A Tribute To Jesse Douglas And Tibor Rado written by Themistocles M Rassias and published by World Scientific. This book was released on 1992-12-21 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Radó. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of Variations, Global Differential Geometry and Global Nonlinear Analysis as related to the problem of Plateau.