Complex Geometry Of Slant Submanifolds
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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.
Contact Geometry Of Slant Submanifolds
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Author : Bang-Yen Chen
language : en
Publisher: Springer Nature
Release Date : 2022-06-27
Contact 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 2022-06-27 with Mathematics categories.
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.
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.
Geometry Of Submanifolds And Applications
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Author : Bang-Yen Chen
language : en
Publisher: Springer Nature
Release Date : 2024-03-26
Geometry Of Submanifolds And Applications 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 2024-03-26 with Mathematics categories.
This book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications. The book covers a wide range of topics such as Chen–Ricci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal η-Ricci–Yamabe solitons, submersion on statistical metallic structure, solitons in f(R, T)-gravity, metric-affine geometry, generalized Wintgen inequalities, tangent bundles, and Lagrangian submanifolds. Moreover, the book showcases the latest findings on Pythagorean submanifolds and submanifolds of four-dimensional f-manifolds. The chapters in this book delve into numerous problems and conjectures on submanifolds, providing valuable insights for scientists, educators, and graduate students looking to stay updated with the latest developments in the field. With its comprehensive coverage and detailed explanations, this book is an essential resource for anyone interested in submanifold theory.
Geometry Of Submanifolds
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Author : Bang-Yen Chen
language : en
Publisher: Courier Dover Publications
Release Date : 2019-06-12
Geometry Of Submanifolds written by Bang-Yen Chen and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Mathematics categories.
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.
Structures On Manifolds
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Author : Masahiro Kon
language : en
Publisher: World Scientific
Release Date : 1985-02-01
Structures On Manifolds written by Masahiro Kon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-02-01 with categories.
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
Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications
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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds. The growing importance of light like hypersurfaces in mathematical physics, in particular their extensive use in relativity, and very limited information available on the general theory of lightlike submanifolds, motivated the present authors, in 1990, to do collaborative research on the subject matter of this book. Based on a series of author's papers (Bejancu [3], Bejancu-Duggal [1,3], Dug gal [13], Duggal-Bejancu [1,2,3]) and several other researchers, this volume was conceived and developed during the Fall '91 and Fall '94 visits of Bejancu to the University of Windsor, Canada. The primary difference between the lightlike submanifold and that of its non degenerate counterpart arises due to the fact that in the first case, the normal vector bundle intersects with the tangent bundle of the submanifold. Thus, one fails to use, in the usual way, the theory of non-degenerate submanifolds (cf. Chen [1]) to define the induced geometric objects (such as linear connection, second fundamental form, Gauss and Weingarten equations) on the light like submanifold. Some work is known on null hypersurfaces and degenerate submanifolds (see an up-to-date list of references on pages 138 and 140 respectively). Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of an up-to-date information on null curves, lightlike hypersur faces and submanifolds, consistent with the theory of non-degenerate submanifolds.
Geometry Of Submanifolds And Homogeneous Spaces
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Author : Andreas Arvanitoyeorgos
language : en
Publisher: MDPI
Release Date : 2020-01-03
Geometry Of Submanifolds And Homogeneous Spaces written by Andreas Arvanitoyeorgos and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.
The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.
Cr Submanifolds Of Kaehlerian And Sasakian Manifolds
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Author : Kentaro Yano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Cr Submanifolds Of Kaehlerian And Sasakian Manifolds written by Kentaro Yano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Riemannian Submersions And Related Topics
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Author : Maria Falcitelli
language : en
Publisher: World Scientific
Release Date : 2004
Riemannian Submersions And Related Topics written by Maria Falcitelli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book provides the first-ever systematic introduction to thetheory of Riemannian submersions, which was initiated by BarrettO''Neill and Alfred Gray less than four decades ago. The authorsfocus their attention on classification theorems when the total spaceand the fibres have nice geometric properties.