riemannian submersions riemannian maps in hermitian geometry and their applications

Riemannian Submersions  Riemannian Maps In Hermitian Geometry  And Their Applications
Author: Bayram Sahin
Publisher: Academic Press
Release Date: 2017-01-23
Pages: 360
ISBN:
Available Language: English, Spanish, And French
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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

Riemannian Submersions And Related Topics
Author: Maria Falcitelli
Publisher: World Scientific
Release Date: 2004-06-21
Pages: 292
ISBN:
Available Language: English, Spanish, And French
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' 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. Contents:Riemannian SubmersionsSubmersions with Totally Geodesic FibresAlmost Hermitian SubmersionsRiemannian Submersions and Contact Metric ManifoldsEinstein Spaces and Riemannian SubmersionsRiemannian Submersions and SubmanifoldsSemi-Riemannian SubmersionsApplications of Riemannian Submersions in Physics Readership: Graduate students and researchers in differential geometry, Riemannian geometry and related fields such as physics. Keywords:Riemannian Submersions;Almost Hermitian Geometry;Contact Metric Manifolds;Einstein Spaces;Semi-Riemannian SubmersionsKey Features:First systematic exposition devoted to Riemannian submersionsDeals with current materialContains a wide-ranging bibliography and about 350 referencesReviews:“The reader should have little difficulty in locating the many different concepts in this rich and rewarding text. Young geometers looking for problems and more importantly directions for future work will find reading this book provides a fine source of material and papers.”Mathematical Reviews “This is a very well-written and interesting book on Riemannian submersions and it is the first monograph in the literature about this topic.”Zentralblatt MATH “Well written, gathering information spread in a lot of papers, unifying the style of many authors, with most of the proofs carried in all details, with a wealth of examples, it certainly fills a gap in the literature and will be a prior reference for both researchers and students.”Romanian Journal of Pure and Applied Mathematics '

Manifolds II
Author: Paul Bracken
Publisher: BoD – Books on Demand
Release Date: 2019-05-22
Pages: 146
ISBN:
Available Language: English, Spanish, And French
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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     Invariants And Applications
Author: Bang-Yen Chen
Publisher: World Scientific
Release Date: 2011-03-23
Pages: 512
ISBN:
Available Language: English, Spanish, And French
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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

Spectral Geometry  Riemannian Submersions  And The Gromov Lawson Conjecture
Author: Peter B. Gilkey
Publisher: CRC Press
Release Date: 1999-07-27
Pages: 296
ISBN:
Available Language: English, Spanish, And French
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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.

Mathematical Reviews
Author:
Publisher:
Release Date: 2004
Pages:
ISBN:
Available Language: English, Spanish, And French
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Revue Roumaine De Math  Matiques Pures Et Appliqu  Es
Author:
Publisher:
Release Date: 2007
Pages:
ISBN:
Available Language: English, Spanish, And French
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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
Author:
Publisher:
Release Date: 1997
Pages:
ISBN:
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The Mathematical Heritage Of C F Gauss
Author: George M Rassias
Publisher: World Scientific
Release Date: 1991-09-30
Pages: 918
ISBN:
Available Language: English, Spanish, And French
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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.

Differential Geometry
Author: Vagn Lundsgaard Hansen
Publisher: Springer
Release Date: 1987-07-15
Pages: 288
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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
Author: George M. Rassias
Publisher:
Release Date: 1985
Pages: 376
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

Papers written by eminent scientists from the international community on the occasion of the 130th anniversary of Henri Poincare's birth (1854-1984).

Stanford Bulletin
Author:
Publisher:
Release Date: 2004
Pages:
ISBN:
Available Language: English, Spanish, And French
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Comprehensive Dissertation Index  Mathematics   Statistics  Physics  A E
Author:
Publisher:
Release Date: 1984
Pages:
ISBN:
Available Language: English, Spanish, And French
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Comprehensive Dissertation Index
Author:
Publisher:
Release Date: 1989
Pages:
ISBN:
Available Language: English, Spanish, And French
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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
Author:
Publisher:
Release Date: 1988
Pages: 834
ISBN:
Available Language: English, Spanish, And French
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Complex Differential Geometry And Nonlinear Differential Equations
Author: Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie
Publisher: Amer Mathematical Society
Release Date: 1986
Pages: 184
ISBN:
Available Language: English, Spanish, And French
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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.

Acta Scientiarum Mathematicarum
Author: József Attila Tudományegyetem
Publisher:
Release Date: 1996
Pages:
ISBN:
Available Language: English, Spanish, And French
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Bollettino Della Unione Matematica Italiana
Author: Unione matematica italiana
Publisher:
Release Date: 1997
Pages:
ISBN:
Available Language: English, Spanish, And French
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Issues In General And Specialized Mathematics Research  2011 Edition
Author:
Publisher: ScholarlyEditions
Release Date: 2012-01-09
Pages: 862
ISBN:
Available Language: English, Spanish, And French
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Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Lectures On Surgical Methods In Rigidity
Author: F. Thomas Farrell
Publisher:
Release Date: 1996
Pages: 98
ISBN:
Available Language: English, Spanish, And French
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