Geometry of Cauchy-Riemann Submanifolds, Dragomir Sorin, Shahid Mohammad Hasan, Al-Solamy Falleh R.
Автор: Chen Bang-yen, Ou Ye-lin Название: Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry ISBN: 9811212376 ISBN-13(EAN): 9789811212376 Издательство: World Scientific Publishing Рейтинг: Цена: 26136.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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.
Автор: Chen Bang-yen Название: Differential Geometry Of Warped Product Manifolds And Submanifolds ISBN: 9813208929 ISBN-13(EAN): 9789813208926 Издательство: World Scientific Publishing Рейтинг: Цена: 26136.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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.
Описание: This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form.
Автор: Alfonso Carriazo, Bogdan D. Suceava, Ivko Dimitric, Joeri Van der Veken, Yun Myung Oh Название: Geometry of Submanifolds ISBN: 1470450925 ISBN-13(EAN): 9781470450922 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 15048.00 р. Наличие на складе: Нет в наличии.
Описание: This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, in honor or Bang-Yen Chen's 75th birthday, held from October 20-21, 2018, at the University of Michigan, Ann Arbor, Michigan. The development of contemporary geometry of submanifolds benefited greatly from Bang-Yen Chen's contributions, as several interesting questions actively pursued today originate in his work. Chen is known for several fundamental ideas in differential geometry, including Chen inequalities, Chen invariants, Chen's conjectures, Chen surface, Chen-Ricci inequality, Chen submanifolds, Chen equality, submanifolds of finite type, and slant submanifolds. The papers in this volume represent a celebration of the geometry of submanifolds and its connections with other areas of mathematics and cover themes rooted in Chen's work, from investigations on the spectrum of the Laplacian on complete Riemannian manifolds to the geometry of symmetric spaces. These contributions are written with the hope to inform and inspire.
Автор: Young Jin Suh; Yoshihiro Ohnita; Jiazu Zhou; Byung Название: Hermitian–Grassmannian Submanifolds ISBN: 9811055556 ISBN-13(EAN): 9789811055553 Издательство: Springer Рейтинг: Цена: 22359.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents the proceedings of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, which was held at the Kyungpook National University from June 21 to 25, 2016. The Workshop was supported by the Research Institute of Real and Complex Manifolds (RIRCM) and the National Research Foundation of Korea (NRF).
Автор: ?lo Lumiste Название: Semiparallel Submanifolds in Space Forms ISBN: 1441923896 ISBN-13(EAN): 9781441923899 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Quite simply, this book is the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, then introduces semiparallel submanifolds and gives some characterizations for their class as well as several subclasses.
Автор: Marcos Dajczer; Ruy Tojeiro Название: Submanifold Theory ISBN: 1493996428 ISBN-13(EAN): 9781493996421 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: Suh Young Jin, Ohnita Yoshihiro, Zhou Jiazu Название: Hermitian-Grassmannian Submanifolds: Daegu, Korea, July 2016 ISBN: 9811354251 ISBN-13(EAN): 9789811354250 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents the proceedings of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, which was held at the Kyungpook National University from June 21 to 25, 2016. The Workshop was supported by the Research Institute of Real and Complex Manifolds (RIRCM) and the National Research Foundation of Korea (NRF).
Автор: Mirjana Djoric; Masafumi Okumura Название: CR Submanifolds of Complex Projective Space ISBN: 1461424771 ISBN-13(EAN): 9781461424772 Издательство: Springer Рейтинг: Цена: 16070.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text begins with an introduction to complex differential geometry and the properties of complex manifolds. It then describes the properties of hypersurfaces of various complex spaces and CR manifolds, emphasizing CR submanifolds of maximal CR dimension.
Автор: Dragomir Название: Geometry of Cauchy-Riemann Submanifolds ISBN: 9811009155 ISBN-13(EAN): 9789811009150 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: Chen Bang-Yen Название: Total Mean Curvature and Submanifolds of Finite Type: 2nd Edition ISBN: 9814616699 ISBN-13(EAN): 9789814616690 Издательство: World Scientific Publishing Рейтинг: Цена: 7128.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds.
Автор: Berndt Название: Submanifolds and Holonomy, Second Edition ISBN: 1482245159 ISBN-13(EAN): 9781482245158 Издательство: Taylor&Francis Рейтинг: Цена: 24499.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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 Edition
New chapter on normal holonomy of complex submanifolds
New chapter on the Berger-Simons holonomy theorem
New chapter on the skew-torsion holonomy system
New chapter on polar actions on symmetric spaces of compact type
New chapter on polar actions on symmetric spaces of noncompact type
New section on the existence of slices and principal orbits for isometric actions
New subsection on maximal totally geodesic submanifolds
New subsection on the index of symmetric spaces
The book uses the reduction of codimension, Moore's lemma for local splitting, and the normal holonomy theorem to address the geometry of submanifolds. It presents a unified treatment of new proofs and main results of homogeneous submanifolds, isoparametric submanifolds, and their generalizations to Riemannian manifolds, particularly Riemannian symmetric spaces.
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