Riemannian Submersions Riemannian Maps In Hermitian Geometry And Their Applications
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Riemannian Submersions Riemannian Maps In Hermitian Geometry And Their Applications
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Author : Bayram Sahin
language : en
Publisher: Academic Press
Release Date : 2017-01-23
Riemannian Submersions Riemannian Maps In Hermitian Geometry And Their Applications written by Bayram Sahin and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Mathematics categories.
Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore's classic 2004 book. In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, also extending their use in Riemannian maps. The work obtains new properties of the domain and target manifolds and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps. - Systematically reviews and references modern literature in Riemannian maps - Provides rigorous mathematical theory with applications - Presented in an accessible reading style with motivating examples that help the reader rapidly progress
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.
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.
Advanced Topics Of Topology
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Author : Francisco Bulnes
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-07-27
Advanced Topics Of Topology written by Francisco Bulnes and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-27 with Mathematics categories.
Topology is an area of mathematics that establishes relations and transformations between spaces with a certain structure depending on their position and considering the structure of the ambient space where these relations exist. This book discusses various concepts and theories of topology, including diffeomorphisms, immersions, Hausdorff spaces, cobordisms, homotopy theory, symplectic manifolds, topology of quantum field theory, algebraic varieties, dimension theory, Koszul complexes, continuum theory, and metrizability, among others.
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.
Differential Geometry And Global Analysis
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Author : Bang-Yen Chen
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-07
Differential Geometry And Global Analysis written by Bang-Yen Chen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-07 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930–2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while recalling historical results, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the $(M_{+}, M_{-})$ method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.
Semi Riemannian Maps And Their Applications
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Author : Eduardo García-Río
language : en
Publisher: Springer
Release Date : 2010-12-08
Semi Riemannian Maps And Their Applications written by Eduardo García-Río and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-08 with Mathematics categories.
A major flaw in semi-Riemannian geometry is a shortage of suitable types of maps between semi-Riemannian manifolds that will compare their geometric properties. Here, a class of such maps called semi-Riemannian maps is introduced. The main purpose of this book is to present results in semi-Riemannian geometry obtained by the existence of such a map between semi-Riemannian manifolds, as well as to encourage the reader to explore these maps. The first three chapters are devoted to the development of fundamental concepts and formulas in semi-Riemannian geometry which are used throughout the work. In Chapters 4 and 5 semi-Riemannian maps and such maps with respect to a semi-Riemannian foliation are studied. Chapter 6 studies the maps from a semi-Riemannian manifold to 1-dimensional semi- Euclidean space. In Chapter 7 some splitting theorems are obtained by using the existence of a semi-Riemannian map. Audience: This volume will be of interest to mathematicians and physicists whose work involves differential geometry, global analysis, or relativity and gravitation.
Manifolds Ii
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Author : Paul Bracken
language : en
Publisher: BoD – Books on Demand
Release Date : 2019-05-22
Manifolds Ii written by Paul Bracken and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-22 with Mathematics categories.
Differential geometry is a very active field of research and has many applications to areas such as physics, in particular gravity. The chapters in this book cover a number of subjects that will be of interest to workers in these areas. It is hoped that these chapters will be able to provide a useful resource for researchers with regard to current fields of research in this important area.
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
Pseudo Riemannian Geometry Delta Invariants And Applications
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Author : Bang-yen Chen
language : en
Publisher: World Scientific
Release Date : 2011-03-23
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 2011-03-23 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 δ-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 δ-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 δ-invariants and the main extrinsic invariants. Since then many new results concerning these δ-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.