Download or read book Riemannian Submersions Riemannian Maps in Hermitian Geometry and their Applications written by Bayram Sahin and published by Academic Press. This book was released on 2017-01-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Semi Riemannian Maps and Their Applications written by Eduardo García-Río and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Complex Geometry of Slant Submanifolds written by Bang-Yen Chen and published by Springer Nature. This book was released on 2022-05-11 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Riemannian Submersions and Related Topics written by Maria Falcitelli and published by World Scientific. This book was released on 2004 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Riemannian Submersions And Related Topics written by Anna Maria Pastore and published by World Scientific. This book was released on 2004-06-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago. The authors focus their attention on classification theorems when the total space and the fibres have nice geometric properties. Particular emphasis is placed on the interrelation with almost Hermitian, almost contact and quaternionic geometry. Examples clarifying and motivating the theory are included in every chapter. Recent results on semi-Riemannian submersions are also explained. Finally, the authors point out the close connection of the subject with some areas of physics.

Download or read book Advanced Topics of Topology written by Francisco Bulnes and published by BoD – Books on Demand. This book was released on 2022-07-27 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1992 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.

Download or read book Differential Geometry and Global Analysis written by Bang-Yen Chen and published by American Mathematical Society. This book was released on 2022-04-07 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Geometry of Submanifolds and Applications written by Bang-Yen Chen and published by Springer Nature. This book was released on with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Selected Topics in Harmonic Maps written by James Eells and published by American Mathematical Soc.. This book was released on 1983-01-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Differential Geometry of Lightlike Submanifolds written by Krishan L. Duggal and published by Springer Science & Business Media. This book was released on 2011-02-02 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.

Download or read book Manifolds II written by Paul Bracken and published by BoD – Books on Demand. This book was released on 2019-05-22 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho and published by Springer. This book was released on 2014-07-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Download or read book Pseudo riemannian Geometry Delta invariants And Applications written by Bang-yen Chen and published by World Scientific. This book was released on 2011-03-23 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Structures On Manifolds written by Masahiro Kon and published by World Scientific. This book was released on 1985-02-01 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Harmonic and Minimal Maps written by Gábor Tóth and published by . This book was released on 1984 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Developments of Harmonic Maps Wave Maps and Yang Mills Fields into Biharmonic Maps Biwave Maps and Bi Yang Mills Fields written by Yuan-Jen Chiang and published by Springer Science & Business Media. This book was released on 2013-06-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.