Total Mean Curvature And Submanifolds Of Finite Type
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Total Mean Curvature And Submanifolds Of Finite Type 2nd Edition
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Author : Bang-yen Chen
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-10-29
Total Mean Curvature And Submanifolds Of Finite Type 2nd Edition written by Bang-yen Chen and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-29 with Mathematics categories.
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.
Total Mean Curvature And Submanifolds Of Finite Type
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Author : Bang-yen Chen
language : en
Publisher: World Scientific Publishing Company
Release Date : 1984
Total Mean Curvature And Submanifolds Of Finite Type written by Bang-yen Chen and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
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
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Author : Bang-yen Chen
language : en
Publisher:
Release Date : 2014
Total Mean Curvature And Submanifolds Of Finite Type 2nd Edition written by Bang-yen Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Electronic books categories.
Complex Geometry Of Slant Submanifolds
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Author : Bang-Yen Chen
language : en
Publisher: Springer Nature
Release Date : 2022-05-11
Complex Geometry Of Slant Submanifolds written by Bang-Yen Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-11 with Mathematics categories.
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.
Prospects Of Differential Geometry And Its Related Fields Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields
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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2013-09-24
Prospects Of Differential Geometry And Its Related Fields Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields written by Toshiaki Adachi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigating these topics and interested in their interdisciplinary areas.
Recent Advances In The Geometry Of Submanifolds
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Author : Bogdan D. Suceavă
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-14
Recent Advances In The Geometry Of Submanifolds written by Bogdan D. Suceavă and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-14 with Mathematics categories.
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.
Geometry And Topology Of Submanifolds Iv Proceedings Of The Conference On Differential Geometry And Vision
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Author : Franki Dillen
language : en
Publisher: World Scientific
Release Date : 1992-07-17
Geometry And Topology Of Submanifolds Iv Proceedings Of The Conference On Differential Geometry And Vision written by Franki Dillen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-07-17 with categories.
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.
Differential Geometry Of Warped Product Manifolds And Submanifolds
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Author : Bang-yen Chen
language : en
Publisher: World Scientific
Release Date : 2017-05-29
Differential Geometry Of Warped Product Manifolds And Submanifolds written by Bang-yen Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-29 with Mathematics categories.
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.
Computer Algebra In Scientific Computing
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Author : Andreas Weber
language : en
Publisher: MDPI
Release Date : 2019-11-04
Computer Algebra In Scientific Computing written by Andreas Weber and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-04 with Computers categories.
Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.
Pseudo Riemannian Geometry Delta Invariants And Applications
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Author : Bang-yen Chen
language : en
Publisher: World Scientific
Release Date : 2011
Pseudo Riemannian Geometry Delta Invariants And Applications written by Bang-yen Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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 ë-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 ë-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 ë-invariants and the main extrinsic invariants. Since then many new results concerning these ë-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.