Differential Equations on Manifolds and Mathematical Physics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Differential Equations on Manifolds and Mathematical Physics PDF full book. Access full book title Differential Equations on Manifolds and Mathematical Physics by Vladimir M. Manuilov. Download full books in PDF and EPUB format.
Author: Vladimir M. Manuilov Publisher: Springer Nature ISBN: 3030373266 Category : Mathematics Languages : en Pages : 349
Book Description
This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.
Author: Vladimir M. Manuilov Publisher: Springer Nature ISBN: 3030373266 Category : Mathematics Languages : en Pages : 349
Book Description
This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.
Author: Gerardo F. Torres del Castillo Publisher: Springer Nature ISBN: 3030451933 Category : Mathematics Languages : en Pages : 447
Book Description
This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics.
Author: Shing-Tung Yau Publisher: Princeton University Press ISBN: 0691082960 Category : Mathematics Languages : en Pages : 720
Book Description
This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.
Author: Yuri E. Gliklikh Publisher: Springer Science & Business Media ISBN: 9401586349 Category : Mathematics Languages : en Pages : 207
Book Description
The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.
Author: Peter Gilkey Publisher: Springer Nature ISBN: 3031023978 Category : Mathematics Languages : en Pages : 159
Book Description
This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible, we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. Math subject classifications : Primary: 53B20 -- (PACS: 02.40.Hw) Secondary: 32Q15, 51F25, 51P05, 53B30, 53C50, 53C80, 58A30, 83F05, 85A04 Table of Contents: Basic Algebraic Notions / Basic Geometrical Notions / Walker Structures / Three-Dimensional Lorentzian Walker Manifolds / Four-Dimensional Walker Manifolds / The Spectral Geometry of the Curvature Tensor / Hermitian Geometry / Special Walker Manifolds
Author: Keti Tenenblat Publisher: Chapman and Hall/CRC ISBN: 9781584880349 Category : Mathematics Languages : en Pages : 224
Book Description
The study of the interaction between differential geometry and partial differential equations has a long history-dating to the last century-and continues to generate considerable interest. Most of the local properties of manifolds are expressed in terms of partial differential equations, and this correspondence proves useful in two ways: we can obtain solutions to the equations from our knowledge about the local geometry of the manifolds, and we can obtain geometric properties of the manifolds-or even prove the non-existence of certain geometric structures on manifolds-from our knowledge of the differential equations. Transformations of Manifolds and Applications to Differential Equations focuses on the role played by differential geometry on the study of differential equations. The author combines the geometric and analytic aspects of the theory, not only in the classical examples, but also in more recent results on integrable systems with an arbitrary number of independent variables. With its applications to problems in evolution equations, strongly hyperbolic systems of the hydrodynamic type, linear Weingarten surfaces, and submanifolds of constant curvature, this volume will prove interesting and valuable to researchers and mathematicians working in differential geometry, differential equations, and mathematical physics.
Author: Jrgen Eichhorn Publisher: World Scientific ISBN: 981277145X Category : Mathematics Languages : en Pages : 353
Book Description
For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.
Author: Gerd Rudolph Publisher: Springer Science & Business Media ISBN: 9400753454 Category : Science Languages : en Pages : 762
Book Description
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Author: Vladimir M. Manuilov
Author: Vladimir M. Manuilov
Author: 
Author: Gerardo F. Torres del Castillo
Author: Shing-Tung Yau
Author: Yuri E. Gliklikh
Author: 
Author: Peter Gilkey
Author: Keti Tenenblat
Author: Jrgen Eichhorn
Author: Gerd Rudolph