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Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications
A Book

by Bayram Sahin

  • Publisher : Academic Press
  • Release : 2017-01-23
  • Pages : 360
  • ISBN : 0128044101
  • Language : En, Es, Fr & De
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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

Manifolds II

Manifolds II
Theory and Applications

by Paul Bracken

  • Publisher : BoD – Books on Demand
  • Release : 2019-05-22
  • Pages : 146
  • ISBN : 1838803092
  • Language : En, Es, Fr & De
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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, δ-Invariants and Applications

Pseudo-Riemannian Geometry, δ-Invariants and Applications
A Book

by Bang-Yen Chen

  • Publisher : World Scientific
  • Release : 2011-03-23
  • Pages : 512
  • ISBN : 9814462489
  • Language : En, Es, Fr & De
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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 Submanifoldsδ-Invariants, Inequalities and Ideal ImmersionsSome Applications of δ-InvariantsApplications to Kähler and Para-Kähler GeometryApplications to Contact GeometryApplications to Affine GeometryApplications to Riemannian SubmersionsNearly Kähler Manifolds and Nearly Kähler S6(1)δ(2)-Ideal Immersions Readership: Graduate and PhD students in differential geometry and related fields; researchers in differential geometry and related fields; theoretical physicists. Keywords:Pseudo-Riemannian Submanifold;δ-Invariants;Spacetimes;Submersion;Lagrangian Submanifolds;Sasakian Manifold;Total Mean Curvature;Submanifold of Finite Type;Affine HypersurfaceKey Features:This is the only book that provides general results on pseudo-Riemannian submanifoldsThis is the only book that provides detailed account on δ-invariantsAt the beginning of each chapter, historical background is providedReviews: “This book gives an extensive and in-depth overview of the theory of pseudo-Riemannian submanifolds and of the delta-invariants. It is written in an accessible and quite self-contained way. Hence it is recommendable for a very broad audience of students and mathematicians interested in the geometry of submanifolds.” Mathematical Reviews “This books is an extensive and comprehensive survey on pseudo–Riemannian submanifolds and δ–invariants as well as their applications. In every aspect, this is an excellent book, invaluable both for learning the topic and a reference. Therefore, it should be strongly recommended for students and mathematicians interested in the geometry of pseudo-Riemannian submanifolds.” Zentralblatt MATH

Mathematical Reviews

Mathematical Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2004
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture

Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture
A Book

by Peter B. Gilkey,John V Leahy,JeongHyeong Park

  • Publisher : CRC Press
  • Release : 1999-07-27
  • Pages : 296
  • ISBN : 9780849382772
  • Language : En, Es, Fr & De
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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 mathematical physics and relativity will find this work both fascinating and important.

Riemannian Submersions and Related Topics

Riemannian Submersions and Related Topics
A Book

by Maria Falcitelli,Anna Maria Pastore,Stere Ianus?

  • Publisher : World Scientific
  • Release : 2004
  • Pages : 277
  • ISBN : 9812562338
  • Language : En, Es, Fr & De
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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.

Revue Roumaine de Mathématiques Pures Et Appliquées

Revue Roumaine de Mathématiques Pures Et Appliquées
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2007
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards

Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1997
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Index of Mathematical Papers

Index of Mathematical Papers
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1973
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Comprehensive Dissertation Index: Mathematics & statistics. Physics, A-E

Comprehensive Dissertation Index: Mathematics & statistics. Physics, A-E
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1984
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Stanford Bulletin

Stanford Bulletin
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2004
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Comprehensive Dissertation Index

Comprehensive Dissertation Index
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1989
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Vols. for 1973- include the following subject areas: Biological sciences, Agriculture, Chemistry, Environmental sciences, Health sciences, Engineering, Mathematics and statistics, Earth sciences, Physics, Education, Psychology, Sociology, Anthropology, History, Law & political science, Business & economics, Geography & regional planning, Language & literature, Fine arts, Library & information science, Mass communications, Music, Philosophy and Religion.

Reviews in Global Analysis, 1980-86 as Printed in Mathematical Reviews

Reviews in Global Analysis, 1980-86 as Printed in Mathematical Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1988
  • Pages : 834
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Differential Geometry

Differential Geometry
Proceedings of the Nordic Summer School held in Lyngby, Denmark, Jul. 29-Aug. 9, 1985

by Vagn Lundsgaard Hansen

  • Publisher : Springer
  • Release : 1987-07-15
  • Pages : 288
  • ISBN : 9783540180128
  • Language : En, Es, Fr & De
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The Nordic Summer School 1985 presented to young researchers the mathematical aspects of the ongoing research stemming from the study of field theories in physics and the differential geometry of fibre bundles in mathematics. The volume includes papers, often with original lines of attack, on twistor methods for harmonic maps, the differential geometric aspects of Yang-Mills theory, complex differential geometry, metric differential geometry and partial differential equations in differential geometry. Most of the papers are of lasting value and provide a good introduction to their subject.

Differential Topology--geometry and Related Fields, and Their Applications to the Physical Sciences and Engineering

Differential Topology--geometry and Related Fields, and Their Applications to the Physical Sciences and Engineering
Dedicated to Henry Poincaré (1854-1912)

by George M. Rassias

  • Publisher : Unknown Publisher
  • Release : 1985
  • Pages : 376
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Acta Scientiarum Mathematicarum

Acta Scientiarum Mathematicarum
A Book

by József Attila Tudományegyetem

  • Publisher : Unknown Publisher
  • Release : 1996
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Bollettino Della Unione Matematica Italiana

Bollettino Della Unione Matematica Italiana
B.

by Unione matematica italiana

  • Publisher : Unknown Publisher
  • Release : 1997
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The Mathematical Heritage of C F Gauss

The Mathematical Heritage of C F Gauss
A Book

by George M Rassias

  • Publisher : World Scientific
  • Release : 1991-09-30
  • Pages : 918
  • ISBN : 9814603791
  • Language : En, Es, Fr & De
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This volume is a collection of original and expository papers in the fields of Mathematics in which Gauss had made many fundamental discoveries. The contributors are all outstanding in their fields and the volume will be of great interest to all research mathematicians, research workers in the history of science, and graduate students in Mathematics and Mathematical Physics. Contents: Powers of 2, Continued Fractions, and the Class Number One Problem for Real Quadratic Fields Q(√d), with d ?1(mod 8) (R A Mollin & H C Williams)A Load Balanced Algorithm for the Calculation of the Polynomial Knot and Link Invariants (B Ewing & K C Millett)The Maxwell Condition in Friedmann Cosmology (C D Hill)Hyper-Kähler Metrics and Monopoles (H Pedersen)Formulas for Higher-Order Finite Expansions of Composite Maps (K P Rybakowski)Gauge-Natural Operators Transforming Connections to the Tangent Bundle (I Kolář)Returns Under Bounded Number of Iterations (Z S Kowalski)The Inequalities with a Small Number of Solutions (J H Evertse & K Gyóry)Factorization in Quaternion Orders Over Number Fields (D R Estes)and other papers Readership: Mathematicians and mathematical physicists.

Complex Differential Geometry and Nonlinear Differential Equations

Complex Differential Geometry and Nonlinear Differential Equations
Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, Held August 12-18, 1984, with Support from the National Science Foundation

by Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie,Yum-Tong Siu

  • Publisher : Amer Mathematical Society
  • Release : 1986
  • Pages : 184
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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This collection of survey articles and research papers focuses on some of the most fruitful methods and ideas in the recently very active field of complex differential geometry and nonlinear differential equations. The topics found in this 1984 Summer Research Conference Proceedings include the local embedding of Cauchy-Riemann structures, minimal varieties, harmonic maps, Chern number inequalities for singular Kahler surfaces, the spectrum of the Laplacian for Kahler manifolds, foliations, vanishing theorems, and complex Finsler metrics. Papers of particular note include Mok's survey on foliation techniques and vanishing theorems, a succinct account of one of the most important methods in several complex variables which has recently produced some very good results, and the research articles by Cheng-Yau and Sampson, which contain highly significant new results. Both researchers and graduate students in the fields of several complex variables, differential geometry, and partial differential equations will find this material especially useful.

Lectures on Surgical Methods in Rigidity

Lectures on Surgical Methods in Rigidity
A Book

by F. Thomas Farrell

  • Publisher : Unknown Publisher
  • Release : 1996
  • Pages : 98
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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An introduction to the topical rigidity theorem for compact non-positively curved Riemannian manifolds, containing an informal account of the background material from surgery theory and controlled topology prerequisite to the result. Written for researchers and advanced graduate students in differential geometry, topology, maths and physics.