Geometry Of Slant Submanifolds

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Complex Geometry of Slant Submanifolds

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Author : Bang-Yen Chen
Publisher : Springer Nature
ISBN 13 : 981160021X
Total Pages : 393 pages
Book Rating : 4.8/5 (116 download)

Book Synopsis Complex Geometry of Slant Submanifolds by : Bang-Yen Chen

Download or read book Complex Geometry of Slant Submanifolds written by Bang-Yen Chen and published by Springer Nature. This book was released on 2022-05-11 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an up-to-date survey and self-contained chapters on complex slant submanifolds and geometry, authored by internationally renowned researchers. The book discusses a wide range of topics, including slant surfaces, slant submersions, nearly Kaehler, locally conformal Kaehler, and quaternion Kaehler manifolds. It provides several classification results of minimal slant surfaces, quasi-minimal slant surfaces, slant surfaces with parallel mean curvature vector, pseudo-umbilical slant surfaces, and biharmonic and quasi biharmonic slant surfaces in Lorentzian complex space forms. Furthermore, this book includes new results on slant submanifolds of para-Hermitian manifolds. This book also includes recent results on slant lightlike submanifolds of indefinite Hermitian manifolds, which are of extensive use in general theory of relativity and potential applications in radiation and electromagnetic fields. Various open problems and conjectures on slant surfaces in complex space forms are also included in the book. It presents detailed information on the most recent advances in the area, making it valuable for scientists, educators and graduate students.

Contact Geometry of Slant Submanifolds

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Author : Bang-Yen Chen
Publisher :
ISBN 13 : 9789811600180
Total Pages : 0 pages
Book Rating : 4.6/5 (1 download)

Book Synopsis Contact Geometry of Slant Submanifolds by : Bang-Yen Chen

Download or read book Contact Geometry of Slant Submanifolds written by Bang-Yen Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Contact Geometry of Slant Submanifolds

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Author : Bang-Yen Chen
Publisher : Springer Nature
ISBN 13 : 9811600171
Total Pages : 372 pages
Book Rating : 4.8/5 (116 download)

Book Synopsis Contact Geometry of Slant Submanifolds by : Bang-Yen Chen

Download or read book Contact Geometry of Slant Submanifolds written by Bang-Yen Chen and published by Springer Nature. This book was released on 2022-06-27 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.

Differential Geometry Of Warped Product Manifolds And Submanifolds

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Author : Bang-yen Chen
Publisher : World Scientific
ISBN 13 : 9813208945
Total Pages : 517 pages
Book Rating : 4.8/5 (132 download)

Book Synopsis Differential Geometry Of Warped Product Manifolds And Submanifolds by : Bang-yen Chen

Download or read book Differential Geometry Of Warped Product Manifolds And Submanifolds written by Bang-yen Chen and published by World Scientific. This book was released on 2017-05-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson-Walker models, are warped product manifolds.The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson-Walker's and Schwarzschild's.The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century.The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.

Geometry of Submanifolds

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Author : Bang-Yen Chen
Publisher : Courier Dover Publications
ISBN 13 : 0486832783
Total Pages : 193 pages
Book Rating : 4.4/5 (868 download)

Book Synopsis Geometry of Submanifolds by : Bang-Yen Chen

Download or read book Geometry of Submanifolds written by Bang-Yen Chen and published by Courier Dover Publications. This book was released on 2019-06-12 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and their applications, and total mean curvature of a submanifold. Suitable for graduate students and mathematicians in the area of classical and modern differential geometries, the treatment is largely self-contained. Problems sets conclude each chapter, and an extensive bibliography provides background for students wishing to conduct further research in this area. This new edition includes the author's corrections.

Structures On Manifolds

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Author : Masahiro Kon
Publisher : World Scientific
ISBN 13 : 9814602809
Total Pages : 520 pages
Book Rating : 4.8/5 (146 download)

Book Synopsis Structures On Manifolds by : Masahiro Kon

Download or read book Structures On Manifolds written by Masahiro Kon and published by World Scientific. This book was released on 1985-02-01 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Riemannian ManifoldsSubmanifolds of Riemannian ManifoldsComplex ManifoldsSubmanifolds of Kaehlerian ManifoldsContact ManifoldsSubmanifolds of Sasakian Manifoldsf-StructuresProduct ManifoldsSubmersions Readership: Mathematicians. Keywords:Riemannian Manifold;Submanifold;Complex Manifold;Contact Manifold;Kaehlerian Manifold;Sasakian Manifold;Anti-Invariant Submanifold;CR Submanifold;Contact CR Submanifold;Submersion

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

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Author : Krishan L. Duggal
Publisher : Springer Science & Business Media
ISBN 13 : 9401720894
Total Pages : 311 pages
Book Rating : 4.4/5 (17 download)

Book Synopsis Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications by : Krishan L. Duggal

Download or read book Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications written by Krishan L. Duggal and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds. The growing importance of light like hypersurfaces in mathematical physics, in particular their extensive use in relativity, and very limited information available on the general theory of lightlike submanifolds, motivated the present authors, in 1990, to do collaborative research on the subject matter of this book. Based on a series of author's papers (Bejancu [3], Bejancu-Duggal [1,3], Dug gal [13], Duggal-Bejancu [1,2,3]) and several other researchers, this volume was conceived and developed during the Fall '91 and Fall '94 visits of Bejancu to the University of Windsor, Canada. The primary difference between the lightlike submanifold and that of its non degenerate counterpart arises due to the fact that in the first case, the normal vector bundle intersects with the tangent bundle of the submanifold. Thus, one fails to use, in the usual way, the theory of non-degenerate submanifolds (cf. Chen [1]) to define the induced geometric objects (such as linear connection, second fundamental form, Gauss and Weingarten equations) on the light like submanifold. Some work is known on null hypersurfaces and degenerate submanifolds (see an up-to-date list of references on pages 138 and 140 respectively). Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of an up-to-date information on null curves, lightlike hypersur faces and submanifolds, consistent with the theory of non-degenerate submanifolds.

Inequalities in Geometry and Applications

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Author : Gabriel-Eduard Vîlcu
Publisher : MDPI
ISBN 13 : 303650298X
Total Pages : 208 pages
Book Rating : 4.0/5 (365 download)

Book Synopsis Inequalities in Geometry and Applications by : Gabriel-Eduard Vîlcu

Download or read book Inequalities in Geometry and Applications written by Gabriel-Eduard Vîlcu and published by MDPI. This book was released on 2021-03-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Geometry And Topology Of Submanifolds Vii: Differential Geometry In Honour Of Prof Katsumi Nomizu

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Author : Franki Dillen
Publisher : World Scientific
ISBN 13 : 9814549460
Total Pages : 334 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Geometry And Topology Of Submanifolds Vii: Differential Geometry In Honour Of Prof Katsumi Nomizu by : Franki Dillen

Download or read book Geometry And Topology Of Submanifolds Vii: Differential Geometry In Honour Of Prof Katsumi Nomizu written by Franki Dillen and published by World Scientific. This book was released on 1995-05-09 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume on pure and applied differential geometry, includes topics on submanifold theory, affine differential geometry and applications of geometry in engineering sciences. The conference was dedicated to the 70th birthday of Prof Katsumi Nomizu. Papers on the scientific work and life of Katsumi Nomizu are also included.

Differential Geometry of Lightlike Submanifolds

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Author : Krishan L. Duggal
Publisher : Springer Science & Business Media
ISBN 13 : 3034602510
Total Pages : 484 pages
Book Rating : 4.0/5 (346 download)

Book Synopsis Differential Geometry of Lightlike Submanifolds by : Krishan L. Duggal

Download or read book Differential Geometry of Lightlike Submanifolds written by Krishan L. Duggal and published by Springer Science & Business Media. This book was released on 2011-02-02 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.

CR Submanifolds of Kaehlerian and Sasakian Manifolds

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Author : Kentaro Yano
Publisher : Springer Science & Business Media
ISBN 13 : 1468494244
Total Pages : 224 pages
Book Rating : 4.4/5 (684 download)

Book Synopsis CR Submanifolds of Kaehlerian and Sasakian Manifolds by : Kentaro Yano

Download or read book CR Submanifolds of Kaehlerian and Sasakian Manifolds written by Kentaro Yano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topics in Modern Differential Geometry

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Author : Stefan Haesen
Publisher : Springer
ISBN 13 : 9462392404
Total Pages : 289 pages
Book Rating : 4.4/5 (623 download)

Book Synopsis Topics in Modern Differential Geometry by : Stefan Haesen

Download or read book Topics in Modern Differential Geometry written by Stefan Haesen and published by Springer. This book was released on 2016-12-21 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

Geometry of Cauchy-Riemann Submanifolds

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Author : Sorin Dragomir
Publisher : Springer
ISBN 13 : 9811009163
Total Pages : 402 pages
Book Rating : 4.8/5 (11 download)

Book Synopsis Geometry of Cauchy-Riemann Submanifolds by : Sorin Dragomir

Download or read book Geometry of Cauchy-Riemann Submanifolds written by Sorin Dragomir and published by Springer. This book was released on 2016-05-31 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

Submanifolds and Holonomy

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Author : Jurgen Berndt
Publisher : CRC Press
ISBN 13 : 1482245167
Total Pages : 494 pages
Book Rating : 4.4/5 (822 download)

Book Synopsis Submanifolds and Holonomy by : Jurgen Berndt

Download or read book Submanifolds and Holonomy written by Jurgen Berndt and published by CRC Press. This book was released on 2016-02-22 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Submanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor.New to the Second EditionNew chapter on normal holonom

Differential Geometry of Slant Surfaces

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Author : Yoshihiko Tazawa
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.3/5 (129 download)

Book Synopsis Differential Geometry of Slant Surfaces by : Yoshihiko Tazawa

Download or read book Differential Geometry of Slant Surfaces written by Yoshihiko Tazawa and published by . This book was released on 1989 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Pseudo-Riemannian Geometry, [delta]-invariants and Applications

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Author : Bang-yen Chen
Publisher : World Scientific
ISBN 13 : 9814329649
Total Pages : 510 pages
Book Rating : 4.8/5 (143 download)

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 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

Riemannian Submersions and Related Topics

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Author : Maria Falcitelli
Publisher : World Scientific
ISBN 13 : 9812388966
Total Pages : 292 pages
Book Rating : 4.8/5 (123 download)

Book Synopsis Riemannian Submersions and Related Topics by : Maria Falcitelli

Download or read book Riemannian Submersions and Related Topics written by Maria Falcitelli and published by World Scientific. This book was released on 2004 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: - First systematic exposition devoted to Riemannian submersions - Deals with current material - Contains a wide-ranging bibliography and about 350 references