Differential Geometry Of Warped Product Manifolds And Submanifolds

Differential Geometry Of Warped Product Manifolds And Submanifolds
Title Differential Geometry Of Warped Product Manifolds And Submanifolds PDF eBook
Author Bang-yen Chen
Publisher World Scientific
Pages 517
Release 2017-05-29
Genre Mathematics
ISBN 9813208945

Download Differential Geometry Of Warped Product Manifolds And Submanifolds Book in PDF, Epub and Kindle

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

Geometry of Submanifolds
Title Geometry of Submanifolds PDF eBook
Author Bang-Yen Chen
Publisher Courier Dover Publications
Pages 193
Release 2019-06-12
Genre Mathematics
ISBN 0486832783

Download Geometry of Submanifolds Book in PDF, Epub and Kindle

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.

Differential Geometry, Algebra, and Analysis

Differential Geometry, Algebra, and Analysis
Title Differential Geometry, Algebra, and Analysis PDF eBook
Author Mohammad Hasan Shahid
Publisher Springer Nature
Pages 284
Release 2020-09-04
Genre Mathematics
ISBN 9811554552

Download Differential Geometry, Algebra, and Analysis Book in PDF, Epub and Kindle

This book is a collection of selected research papers, some of which were presented at the International Conference on Differential Geometry, Algebra and Analysis (ICDGAA 2016), held at the Department of Mathematics, Jamia Millia Islamia, New Delhi, from 15–17 November 2016. It covers a wide range of topics—geometry of submanifolds, geometry of statistical submanifolds, ring theory, module theory, optimization theory, and approximation theory—which exhibit new ideas and methodologies for current research in differential geometry, algebra and analysis. Providing new results with rigorous proofs, this book is, therefore, of much interest to readers who wish to learn new techniques in these areas of mathematics.

Structures On Manifolds

Structures On Manifolds
Title Structures On Manifolds PDF eBook
Author Masahiro Kon
Publisher World Scientific
Pages 520
Release 1985-02-01
Genre
ISBN 9814602809

Download Structures On Manifolds Book in PDF, Epub and Kindle

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

Complex Geometry of Slant Submanifolds

Complex Geometry of Slant Submanifolds
Title Complex Geometry of Slant Submanifolds PDF eBook
Author Bang-Yen Chen
Publisher Springer Nature
Pages 393
Release 2022-05-11
Genre Mathematics
ISBN 981160021X

Download Complex Geometry of Slant Submanifolds Book in PDF, Epub and Kindle

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.

Riemannian Manifolds

Riemannian Manifolds
Title Riemannian Manifolds PDF eBook
Author John M. Lee
Publisher Springer Science & Business Media
Pages 232
Release 2006-04-06
Genre Mathematics
ISBN 0387227261

Download Riemannian Manifolds Book in PDF, Epub and Kindle

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Contact Geometry of Slant Submanifolds

Contact Geometry of Slant Submanifolds
Title Contact Geometry of Slant Submanifolds PDF eBook
Author Bang-Yen Chen
Publisher Springer Nature
Pages 372
Release 2022-06-27
Genre Mathematics
ISBN 9811600171

Download Contact Geometry of Slant Submanifolds Book in PDF, Epub and Kindle

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.