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Geometry Of Complete Riemannian Submanifolds
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Book Synopsis Foliations on Riemannian Manifolds and Submanifolds by : Vladimir Rovenski
Download or read book Foliations on Riemannian Manifolds and Submanifolds written by Vladimir Rovenski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.
Book Synopsis Geometry of Complete Riemannian Submanifolds by : Bao Qiang Wu
Download or read book Geometry of Complete Riemannian Submanifolds written by Bao Qiang Wu and published by . This book was released on 1998 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: La géométrie rienmannienne des sous-variétés a connu ces cinquante dernières années un essor considérable, essentiellement dans le cas compact. Cette thèse a pour but de développer des outils consacrés à l'étude des sous-variétés riemanniennes complètes. Ces outils sont proches de ceux développés par Bochner et Lichnérowicz. Ils sont particulièrement adaptés aux problèmes de rigidité de certains types de sous-variétés complètes : celles qui sont à courbure moyenne constante dans un espace hyperbolique. Il est ainsi possible d'obtenir un théorème de classification de ces sous-variétés. D'autres applications sont données pour des sous-variétés totalement réelles des espaces projectifs complexes.
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
Book Synopsis Differential Geometry of Submanifolds by : K. Kenmotsu
Download or read book Differential Geometry of Submanifolds written by K. Kenmotsu and published by Springer. This book was released on 2007-01-05 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry of Manifolds by : K. Shiohama
Download or read book Geometry of Manifolds written by K. Shiohama and published by Elsevier. This book was released on 1989-10-04 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at a symposium on differential geometry at Shinshu University in July of 1988. Carefully reviewed by a panel of experts, the papers pertain to the following areas of research: dynamical systems, geometry of submanifolds and tensor geometry, lie sphere geometry, Riemannian geometry, Yang-Mills Connections, and geometry of the Laplace operator.
Book Synopsis Geometry of CR-Submanifolds by : Aurel Bejancu
Download or read book Geometry of CR-Submanifolds written by Aurel Bejancu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can us;; Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Submanifold Theory by : Marcos Dajczer
Download or read book Submanifold Theory written by Marcos Dajczer and published by Springer. This book was released on 2019-08-02 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms. One main theme is the isometric and conformal deformation problem for submanifolds of arbitrary dimension and codimension. Several relevant classes of submanifolds are also discussed, including constant curvature submanifolds, submanifolds of nonpositive extrinsic curvature, conformally flat submanifolds and real Kaehler submanifolds. This is the first textbook to treat a substantial proportion of the material presented here. The first chapters are suitable for an introductory course on Submanifold theory for students with a basic background on Riemannian geometry. The remaining chapters could be used in a more advanced course by students aiming at initiating research on the subject, and are also intended to serve as a reference for specialists in the field.
Book Synopsis The Geometry of Submanifolds by : Yu. Aminov
Download or read book The Geometry of Submanifolds written by Yu. Aminov and published by CRC Press. This book was released on 2001-01-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects. Discussions include submanifolds in Euclidean states and Riemannian space, minimal submanifolds, Grassman mappings, multi-dimensional regular polyhedra, and isometric immersions of Lobachevski space into Euclidean spaces. This volume also highlights the contributions made by great geometers to the geometry of submanifolds and its areas of application.
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.
Book Synopsis Riemannian Geometry by : Sylvestre Gallot
Download or read book Riemannian Geometry written by Sylvestre Gallot and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. It treats in detail classical results on the relations between curvature and topology. The book features numerous exercises with full solutions and a series of detailed examples are picked up repeatedly to illustrate each new definition or property introduced.
Book Synopsis Comparison Theorems in Riemannian Geometry by : Jeff Cheeger
Download or read book Comparison Theorems in Riemannian Geometry written by Jeff Cheeger and published by Newnes. This book was released on 1975 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis The Geometry of Submanifolds by : Yu. Aminov
Download or read book The Geometry of Submanifolds written by Yu. Aminov and published by CRC Press. This book was released on 2001-01-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects.
Book Synopsis Geometry of Submanifolds and Applications by : Bang-Yen Chen
Download or read book Geometry of Submanifolds and Applications written by Bang-Yen Chen and published by Springer Nature. This book was released on with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimal Submanifolds in Pseudo-Riemannian Geometry by : Henri Anciaux
Download or read book Minimal Submanifolds in Pseudo-Riemannian Geometry written by Henri Anciaux and published by World Scientific. This book was released on 2011 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case. For the first time, this textbook provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory. Several classical results, such as the Weierstrass representation formula for minimal surfaces, and the minimizing properties of complex submanifolds, are presented in full generality without sacrificing the clarity of exposition. Finally, a number of very recent results on the subject, including the classification of equivariant minimal hypersurfaces in pseudo-Riemannian space forms and the characterization of minimal Lagrangian surfaces in some pseudo-Khler manifolds are given.
Book Synopsis Geometric Analysis of Quasilinear Inequalities on Complete Manifolds by : Bruno Bianchini
Download or read book Geometric Analysis of Quasilinear Inequalities on Complete Manifolds written by Bruno Bianchini and published by Springer Nature. This book was released on 2021-01-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Book Synopsis Tight and Taut Submanifolds by : Nicolaas Hendrik Kuiper
Download or read book Tight and Taut Submanifolds written by Nicolaas Hendrik Kuiper and published by Cambridge University Press. This book was released on 1997-11-13 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1997, this book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The book is dedicated to the memory of Nicolaas H. Kuiper; the first paper is an unfinished but insightful survey of the field of tight immersions and maps written by Kuiper himself. Other papers by leading researchers in the field treat topics such as the smooth and polyhedral portions of the theory of tight immersions, taut, Dupin and isoparametric submanifolds of Euclidean space, taut submanifolds of arbitrary complete Riemannian manifolds, and real hypersurfaces in complex space forms with special curvature properties. Taken together these articles provide a comprehensive survey of the field and point toward several directions for future research.
