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Author: Jurgen Berndt
Publisher: CRC Press
ISBN: 1482245167
Category : Mathematics
Languages : en
Pages : 494
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Book Description
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
Author: Jurgen Berndt
Publisher: CRC Press
ISBN: 1482245167
Category : Mathematics
Languages : en
Pages : 494
Get Book
Book Description
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
Author: Jurgen Berndt
Publisher: Chapman and Hall/CRC
ISBN: 9781584883715
Category : Mathematics
Languages : en
Pages : 352
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Book Description
With special emphasis on new techniques based on the holonomy of the normal connection, this book provides a modern, self-contained introduction to submanifold geometry. It offers a thorough survey of these techniques and their applications and presents a framework for various recent results to date found only in scattered research papers. The treatment introduces all the basics of the subject, and along with some classical results and hard-to-find proofs, presents new proofs of several recent results. Appendices furnish the necessary background material, exercises give readers practice in using the techniques, and discussion of open problems stimulates readers' interest in the field.
Author: Dominic D. Joyce
Publisher: Oxford University Press
ISBN: 019921560X
Category : Mathematics
Languages : en
Pages : 314
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Book Description
Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
Author: Dominic D. Joyce
Publisher: OUP Oxford
ISBN: 9780198506010
Category : Mathematics
Languages : en
Pages : 460
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Book Description
This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.
Author: Bang-Yen Chen
Publisher: Courier Dover Publications
ISBN: 0486832783
Category : Mathematics
Languages : en
Pages : 193
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Book Description
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.
Author: Bogdan D. Suceavă
Publisher: American Mathematical Soc.
ISBN: 1470422980
Category : Differential geometry -- Local differential geometry -- Local submanifolds
Languages : en
Pages : 209
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Book Description
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.
Author: Luc Vrancken
Publisher: Lulu.com
ISBN: 1847990169
Category :
Languages : en
Pages : 266
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Book Description
This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).
Author: Y. L. Xin
Publisher: World Scientific
ISBN: 9812386874
Category : Mathematics
Languages : en
Pages : 271
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Book Description
The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimensions. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
Author: Franki Dillen
Publisher: World Scientific
ISBN: 9814550655
Category :
Languages : en
Pages : 324
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Book Description
The topics covered are pure differential geometry, especially submanifolds and affine differential geometry, and applications of geometry to human vision, robotics, and gastro-entrology. Contents:A Riemannian Invariant for Submanifolds in Space Forms and Its Applications (B Y Chen)Some Variational Problems in Submanifold Theory (F Dillen)Isoparametric Systems on Symmetric Spaces (S Mullen)Focal Sets in Affine Geometry (R Niebergall P J Ryan)Buckling Eigenvalues and Variational Problems for Surfaces in the Three Sphere (B Palmer)On Completeness of Compact Lorentzian Manifolds (A Romero & M Sánchez)On Para Sasakian Manifolds (R Rosca)A Unified Equiaffine Theory for Surfaces in R4, Part 1: The Definite Surfaces (C P Wang)Cartan's Method of Moving Frames Applied to the Study of Surfaces in Affine 4-Space (J L Weiner)A Survey on the Theory of Harmonic (Pseudo)-Riemannian Spaces (T J Willmore)Human Representation of Closed Contours (K Waeytens et al)Affine Shape Equivalence (J Wagemans et al)and other papers Readership: Mathematicians and engineers. keywords:
Author: Marcos Dajczer
Publisher: Springer
ISBN: 1493996444
Category : Mathematics
Languages : en
Pages : 628
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Book Description
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.
