Riemannian Submersions  Riemannian Maps in Hermitian Geometry  and their Applications Book

Riemannian Submersions Riemannian Maps in Hermitian Geometry and their Applications


  • Author : Bayram Sahin
  • Publisher : Academic Press
  • Release Date : 2017-01-23
  • Genre: Mathematics
  • Pages : 360
  • ISBN 10 : 9780128044100

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Riemannian Submersions Riemannian Maps in Hermitian Geometry and their Applications 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

Differential Geometry and Global Analysis Book

Differential Geometry and Global Analysis


  • Author : Bang-Yen Chen
  • Publisher : American Mathematical Society
  • Release Date : 2022-04-07
  • Genre: Mathematics
  • Pages : 242
  • ISBN 10 : 9781470460150

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Differential Geometry and Global Analysis 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.

Riemannian Submersions and Related Topics Book

Riemannian Submersions and Related Topics


  • Author : Maria Falcitelli
  • Publisher : World Scientific
  • Release Date : 2004
  • Genre: Mathematics
  • Pages : 277
  • ISBN 10 : 9789812562333

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Riemannian Submersions and Related Topics 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.

Manifolds II Book

Manifolds II


  • Author : Paul Bracken
  • Publisher : BoD – Books on Demand
  • Release Date : 2019-05-22
  • Genre: Mathematics
  • Pages : 146
  • ISBN 10 : 9781838803094

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Manifolds II 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.

Pseudo Riemannian Geometry     Invariants and Applications Book

Pseudo Riemannian Geometry Invariants and Applications


  • Author : Bang-Yen Chen
  • Publisher : World Scientific
  • Release Date : 2011-03-23
  • Genre: Mathematics
  • Pages : 512
  • ISBN 10 : 9789814462488

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Pseudo Riemannian Geometry Invariants and Applications 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. Contents:Pseudo-Riemannian ManifoldsBasics on Pseudo-Riemannian SubmanifoldsSpecial Pseudo-Riemannian SubmanifoldsWarped Products and Twisted ProductsRobertson–Walker SpacetimesHodge Theory, Elliptic Differential Operators and Jacobi's Elliptic FunctionsSubmanifolds of Finite TypeTotal Mean CurvaturePseudo-Kähler ManifoldsPara-Kähler ManifoldsPseudo-Riemannian SubmersionsContact Metric Manifolds and Submanifol

Spectral Geometry  Riemannian Submersions  and the Gromov Lawson Conjecture Book

Spectral Geometry Riemannian Submersions and the Gromov Lawson Conjecture


  • Author : Peter B. Gilkey
  • Publisher : CRC Press
  • Release Date : 1999-07-27
  • Genre: Mathematics
  • Pages : 296
  • ISBN 10 : 0849382777

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Spectral Geometry Riemannian Submersions and the Gromov Lawson Conjecture Excerpt :

This cutting-edge, standard-setting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian and pi: Z ® Y is a Riemannian submersion. After providing the necessary background, including basic differential geometry and a discussion of Laplace type operators, the authors address rigidity theorems. They establish conditions that ensure that the pull back of every eigenform on Y is an eigenform on Z so the eigenvalues do not change, then show that if a single eigensection is preserved, the eigenvalues do not change for the scalar or Bochner Laplacians. For the form valued Laplacian, they show that if an eigenform is preserved, then the corresponding eigenvalue can only increase. They generalize these results to the complex setting as well. However, the spinor setting is quite different. For a manifold with non-trivial boundary and imposed Neumann boundary conditions, the result is surprising-the eigenvalues can change. Although this is a relatively rare phenomenon, the authors give examples-a circle bundle or, more generally, a principal bundle with structure group G where the first cohomology group H1(G;R) is non trivial. They show similar results in the complex setting, show that eigenvalues can decrease in the spinor setting, and offer a list of unsolved problems in this area. Moving to some related topics involving questions of positive curvature, for the first time in mathematical literature the authors establish a link between the spectral geometry of Riemannian submersions and the Gromov-Lawson conjecture. Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture addresses a hot research area and promises to set a standard for the field. Researchers and applied mathematicians interested in math

Semi Riemannian Geometry With Applications to Relativity Book
Score: 4
From 2 Ratings

Semi Riemannian Geometry With Applications to Relativity


  • Author : Barrett O'Neill
  • Publisher : Academic Press
  • Release Date : 1983-07-29
  • Genre: Mathematics
  • Pages : 468
  • ISBN 10 : 9780080570570

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Semi Riemannian Geometry With Applications to Relativity Excerpt :

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

Differential Geometry of Lightlike Submanifolds Book

Differential Geometry of Lightlike Submanifolds


  • Author : Krishan L. Duggal
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-02-02
  • Genre: Mathematics
  • Pages : 488
  • ISBN 10 : 9783034602518

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Differential Geometry of Lightlike Submanifolds 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.

Semi Riemannian Maps and Their Applications Book

Semi Riemannian Maps and Their Applications


  • Author : Eduardo García-Río
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Mathematics
  • Pages : 198
  • ISBN 10 : 9789401729796

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Semi Riemannian Maps and Their Applications 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.

Harmonic Morphisms Between Riemannian Manifolds Book

Harmonic Morphisms Between Riemannian Manifolds


  • Author : Paul Baird
  • Publisher : Oxford University Press
  • Release Date : 2003
  • Genre: Mathematics
  • Pages : 520
  • ISBN 10 : 0198503628

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Harmonic Morphisms Between Riemannian Manifolds Excerpt :

This is the first account in book form of the theory of harmonic morphisms between Riemannian manifolds. Harmonic morphisms are maps which preserve Laplace's equation. They can be characterized as harmonic maps which satisfy an additional first order condition. Examples include harmonic functions, conformal mappings in the plane, and holomorphic functions with values in a Riemann surface. There are connections with many concepts in differential geometry, for example, Killing fields, geodesics, foliations, Clifford systems, twistor spaces, Hermitian structures, iso-parametric mappings, and Einstein metrics and also the Brownain pathpreserving maps of probability theory. Giving a complete account of the fundamental aspects of the subject, this book is self-contained, assuming only a basic knowledge of differential geometry.

Encyclopaedia of Mathematics Book
Score: 4
From 1 Ratings

Encyclopaedia of Mathematics


  • Author : Michiel Hazewinkel
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 632
  • ISBN 10 : 9789401512794

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Encyclopaedia of Mathematics Excerpt :

This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Geometry of Cauchy Riemann Submanifolds Book

Geometry of Cauchy Riemann Submanifolds


  • Author : Sorin Dragomir
  • Publisher : Springer
  • Release Date : 2016-05-31
  • Genre: Mathematics
  • Pages : 390
  • ISBN 10 : 9789811009167

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Geometry of Cauchy Riemann Submanifolds Excerpt :

This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

Two Reports on Harmonic Maps Book

Two Reports on Harmonic Maps


  • Author : James Eells
  • Publisher : World Scientific
  • Release Date : 1995-03-29
  • Genre: Mathematics
  • Pages : 228
  • ISBN 10 : 9789814502924

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Two Reports on Harmonic Maps Excerpt :

Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, σ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kählerian manifolds. A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire. This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers. Contents:IntroductionOperations on Vector BundlesHarmonic MapsComposition PropertiesMaps into Manifolds of Nonpositive (≤ 0) CurvatureThe Existence Theorem for Riem N ≤ 0Maps into Flat ManifoldsHarmonic Maps between SpheresHolomorphic MapsHarmonic Maps of a SurfaceHarmonic Maps between SurfacesHarmonic Maps of Manifolds with Boundary Readership: Mathematicians and mathematical physicists. keywords:Harmonic Maps;Minimal Immersions;Totally Geodesic Maps;Kaehler Manifold;(1,1)-Geodesic Map;Dilatation;Nonpositive Sectional Curvature;Holomorphic Map;Teichmueller Map;Twistor Construction “… an interesting account of the progress made in the theory of harmonic maps until the year 1988 … this master-piece work will serve as an influence and good reference in the very active subject of harmonic maps both from the points of view of theory and applications.” Mathematics Abstracts

Mathematical Reviews Book

Mathematical Reviews


  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2004
  • Genre: Mathematics
  • Pages : null
  • ISBN 10 : UOM:39015059777659

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Mathematical Reviews Excerpt :