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Kahler Immersions Of Kahler Manifolds Into Complex Space Forms
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Book Synopsis Kähler Immersions of Kähler Manifolds into Complex Space Forms by : Andrea Loi
Download or read book Kähler Immersions of Kähler Manifolds into Complex Space Forms written by Andrea Loi and published by Springer. This book was released on 2018-09-20 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to describe Calabi's original work on Kähler immersions of Kähler manifolds into complex space forms, to provide a detailed account of what is known today on the subject and to point out some open problems. Calabi's pioneering work, making use of the powerful tool of the diastasis function, allowed him to obtain necessary and sufficient conditions for a neighbourhood of a point to be locally Kähler immersed into a finite or infinite-dimensional complex space form. This led to a classification of (finite-dimensional) complex space forms admitting a Kähler immersion into another, and to decades of further research on the subject. Each chapter begins with a brief summary of the topics to be discussed and ends with a list of exercises designed to test the reader's understanding. Apart from the section on Kähler immersions of homogeneous bounded domains into the infinite complex projective space, which could be skipped without compromising the understanding of the rest of the book, the prerequisites to read this book are a basic knowledge of complex and Kähler geometry.
Book Synopsis Lectures on Kähler Manifolds by : Werner Ballmann
Download or read book Lectures on Kähler Manifolds written by Werner Ballmann and published by European Mathematical Society. This book was released on 2006 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on lectures the author gave at the University of Bonn and the Erwin Schrodinger Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kahler manifolds. The more advanced topics are the cohomology of Kahler manifolds, Calabi conjecture, Gromov's Kahler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern-Weil theory, symmetric spaces, and $L^2$-cohomology.
Book Synopsis Handbook of Differential Geometry, Volume 1 by : F.J.E. Dillen
Download or read book Handbook of Differential Geometry, Volume 1 written by F.J.E. Dillen and published by Elsevier. This book was released on 1999-12-16 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Book Synopsis Issues in General and Specialized Mathematics Research: 2013 Edition by :
Download or read book Issues in General and Specialized Mathematics Research: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1919 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book 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: 2013 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/.
Book Synopsis Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics by : Stancho Dimiev
Download or read book Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics written by Stancho Dimiev and published by World Scientific. This book was released on 2007 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas. Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.
Book Synopsis Prospects in Complex Geometry by : Junjiro Noguchi
Download or read book Prospects in Complex Geometry written by Junjiro Noguchi and published by Springer. This book was released on 2006-11-14 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Teichmüller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years. Thus the central subject of "Complex Structure" was a timely choice for the joint meetings in Katata and Kyoto in 1989. The invited participants exchanged ideas on different approaches to related topics in complex geometry and mapped out the prospects for the next few years of research.
Book Synopsis Trends in Complex Analysis, Differential Geometry, and Mathematical Physics by : Stancho Dimiev
Download or read book Trends in Complex Analysis, Differential Geometry, and Mathematical Physics written by Stancho Dimiev and published by World Scientific. This book was released on 2003 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers.
Book Synopsis Differential Geometry Of Warped Product Manifolds And Submanifolds by : Chen Bang-yen
Download or read book Differential Geometry Of Warped Product Manifolds And Submanifolds written by Chen Bang-yen and published by World Scientific. This book was released on 2017-05-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson–Walker models, are warped product manifolds. The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson–Walker's and Schwarzschild's. The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Book Synopsis Trends in Complex Analysis, Differential Geometry and Mathematical Physics by : Stancho Dimiev
Download or read book Trends in Complex Analysis, Differential Geometry and Mathematical Physics written by Stancho Dimiev and published by World Scientific. This book was released on 2003-06-13 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers. Contents:Real Analytic Almost Complex Manifolds (L N Apostolova)Involutive Distributions of Codimension One in Kaehler Manifolds (G Ganchev)Three Theorems on Isotropic Immersions (S Maeda)On the Meilikhson Theorem (M S Marinov)Curvature Tensors on Almost Contact Manifolds with B-Metric (G Nakova)Complex Structures and the Quark Confinement (I B Pestov)Curvature Operators in the Relativity (V Videv & Y Tsankov)On Integrability of Almost Quaternionic Manifolds (A Yamada)and other papers Readership: Graduate students and researchers in complex analysis, differential geometry and mathematical physics. Keywords:Poincare Formulae;Oka''s Theorem;Quantum Field Theory;Time-Like Killing Vector Field;Kaehler Immersion;Circle;Integrability of Almost Hermitian Manifold;Hyperocmplex Manifold;Semi-Symmetric Space;Hypercomplex Manifold'
Book Synopsis Toeplitz Operators on Kähler Manifolds by : Tatyana Barron
Download or read book Toeplitz Operators on Kähler Manifolds written by Tatyana Barron and published by Springer. This book was released on 2018-07-24 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this Brief is to give a quick practical introduction into the subject of Toeplitz operators on Kähler manifolds, via examples, worked out carefully and in detail. Necessary background is included. Several theorems on asymptotics of Toeplitz operators are reviewed and illustrated by examples, including the case of tori and the 2-dimensional sphere. Applications in the context of multisymplectic and hyperkähler geometry are discussed. The book is suitable for graduate students, advanced undergraduate students, and any researchers.
Book Synopsis Nearly Pseudo-Kähler Manifolds and Related Special Holonomies by : Lars Schäfer
Download or read book Nearly Pseudo-Kähler Manifolds and Related Special Holonomies written by Lars Schäfer and published by Springer. This book was released on 2017-09-14 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing and providing an overview of recent results on nearly Kähler geometry on pseudo-Riemannian manifolds, this monograph emphasizes the differences with the classical Riemannian geometry setting. The focal objects of the text are related to special holonomy and Killing spinors and have applications in high energy physics, such as supergravity and string theory. Before starting into the field, a self-contained introduction to the subject is given, aimed at students with a solid background in differential geometry. The book will therefore be accessible to masters and Ph.D. students who are beginning work on nearly Kähler geometry in pseudo-Riemannian signature, and also to non-experts interested in gaining an overview of the subject. Moreover, a number of results and techniques are provided which will be helpful for differential geometers as well as for high energy physicists interested in the mathematical background of the geometric objects they need.
Book Synopsis Contemporary Geometry by : Hung-Hsi Wu
Download or read book Contemporary Geometry written by Hung-Hsi Wu and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early one morning in April of 1987, the Chinese mathematician J. -Q. Zhong died unexpectedly of a heart attack in New York. He was then near the end of a one-year visit in the United States. When news of his death reached his Chinese-American friends, it was immediately decided by one and all that something should be done to preserve his memory. The present volume is an outgrowth of this sentiment. His friends in China have also established a Zhong Jia-Qing Memorial Fund, which has since twice awarded the Zhong Jia-Qing prizes for Chinese mathematics graduate students. It is hoped that at least part of the reasons for the esteem and affection in which he was held by all who knew him would come through in the succeeding pages of this volume. The three survey chapters by Li and Treibergs, Lu, and Siu (Chapters 1-3) all center around the areas of mathematics in which Zhong made noteworthy contributions. In addition to putting Zhong's mathematical contributions in perspective, these articles should be useful also to a large segment of the mathematical community; together they give a coherent picture of a sizable portion of contemporary geometry. The survey of Lu differs from the other two in that it gives a firsthand account of the work done in the People's Republic of China in several complex variables in the last four decades.
Book Synopsis Differential Geometry of Submanifolds and its Related Topics by : Sadahiro Maeda
Download or read book Differential Geometry of Submanifolds and its Related Topics written by Sadahiro Maeda and published by World Scientific. This book was released on 2013-10-23 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form. Contents:Homogeneous Submanifolds and Homogeneous Curves in Space Forms (S Maeda)Injectivity Property of Regular Curves and a Sphere Theorem (O Kobayashi)A Family of Complete Minimal Surfaces of Finite Total Curvature with Two Ends (S Fujimori and T Shoda)Minimal Surfaces in the Anti-De Sitter Spacetime (T Ichiyama and S Udagawa)Extrinsic Circular Trajectories on Geodesic Spheres in a Complex Projective Space (T Adachi)Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces (Y Ohnita)Some Real Hypersurfaces of Complex Projective Space (T Hamada)Contact Metric Hypersurfaces in Complex Space Forms (J T Cho and J Inoguchi)Non-Homogeneous η-Einstein Real Hypersurfaces in a 2-Dimensional Nonflat Complex Space Form (K Okumura)Sectional Curvatures of Ruled Real Hypersurfaces in a Nonflat Complex Space Form (H Tanabe and S Maeda)Totally Geodesic Köhler Immersions into a Complex Space Form, and a Non-Existence Theorem for Hessian Metrics of Positive Constant Hessian Sectional Curvature (T Noda and N Boumuki)Archimedean Theorems and W-Curves (D-S Kim and Y H Kim)On the Construction of Cohomogeneity One Special Lagrangian Submanifolds in the Cotangent Bundle of the Sphere (K Hashimoto)Self-Shrinkers of the Mean Curvature Flow (Q-M Cheng and Y Peng)Spectrum of Poly-Laplacian and Fractional Laplacian (L Zeng)Flat Centroaffine Surfaces with Non-Semisimple Tchebychev Operator (A Fujioka)The Total Absolute Curvature of Open Curves in EN (K Enomoto and J Itoh)Antipodal Sets of Compact Symmetric Spaces and the Intersection of Totally Geodesic Submanifolds (M S Tanaka)A Note on Symmetric Triad and Hermann Action (O Ikawa)Some Topics of Homogeneous Submanifolds in Complex Hyperbolic Spaces (T Hashinaga, A Kubo and H Tamaru)Austere Hypersurfaces in 5-Sphere and Real Hypersurfaces in Complex Projective Plane (J T Cho and M Kimura)On the Minimality of Normal Bundles in the Tangent Bundles Over the Complex Space Forms (T Kajigaya)Over-Determined Systems on Surfaces (N Ando) Readership: Researchers in differential geometry. Keywords:Minimal Surfaces;Morse Index;Real Hypersurfaces;Non-flat Complex Space Forms;Hopf Hypersurfaces;Symmetric Spaces;Homogeneous CurvesKey Features:Interesting papers on the theory of real hypersurfaces and the theory of minimal surfacesFeatures prominent contributors such as Y Ohnita, Q-M Cheng and O Kobayashi
Book Synopsis Analysis and Geometry by : Ali Baklouti
Download or read book Analysis and Geometry written by Ali Baklouti and published by Springer. This book was released on 2015-07-26 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of Mohammed Salah Baouendi, a most renowned figure in the field of several complex variables, who passed away in 2011. All research articles were written by leading experts, some of whom are prize winners in the fields of complex geometry, algebraic geometry and analysis. The book offers a valuable resource for all researchers interested in recent developments in analysis and geometry.
Book Synopsis Complex Geometry of Slant Submanifolds by : Bang-Yen Chen
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.
Book Synopsis Complex, Contact and Symmetric Manifolds by : Oldrich Kowalski
Download or read book Complex, Contact and Symmetric Manifolds written by Oldrich Kowalski and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Contains research and survey articles by well known and respected mathematicians on recent developments and research trends in differential geometry and topology * Dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields * Papers include all necessary introductory and contextual material to appeal to non-specialists, as well as researchers and differential geometers
Book Synopsis Two Reports on Harmonic Maps by : James Eells
Download or read book Two Reports on Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1995-03-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book 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
