Differential Manifolds

Cover of: Differential Manifolds | Serge Lang

Published by Springer .

Written in English

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The Physical Object
Number of Pages230
ID Numbers
Open LibraryOL7449069M
ISBN 100387961135
ISBN 109780387961132

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Don't be deceived by the title of Kosinski's "Differential Manifolds," which sounds like a book covering differential forms, such as Lee's Introduction to Smooth Manifolds, or by claims that it is self-contained or for beginning graduate fact, the purpose of this book is Differential Manifolds book lay out the theory of (higher-dimensional, i.e., >= 5) smooth manifolds as it was known in the '60s, namely /5(6).

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a Cited by: 4.

The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different contexts.

The foreword which I wrote in the earlier book. A little bit more advanced and dealing extensively with differential geometry of manifolds is the book by Jeffrey Lee - "Manifolds and Differential Geometry" (do not confuse it with the other books by John M.

Lee which are also nice but too many and too long to cover the same material for my tastes). You can use it as a complement to Tu's or as.

Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics.

The book has proven to be an excellent introduction to the theory of complex manifolds considered from both the points of view of complex analysis and differential geometry.” (Philosophy, Religion and Science Book Reviews,May, ).

Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general. The book provides a broad introduction to the field of differentiable and Riemannian manifolds, tying.

"How useful it is," noted the Bulletin of the American Mathematical Society, "to have a single, short, well-written book on differential topology." This accessible volume introduces advanced Differential Manifolds book and graduate students the systematic study of the topological structure of smooth manifolds, from elements of theory to method of surgery.

edition. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds.

An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean s: 1. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds.

Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential. - Differential Manifolds by Lang, Serge. You Searched For: ISBN: This is an ex-library book and may Differential Manifolds book the usual library/used-book markings book has hardback covers.

In good all round condition. Please note the Image in this listing is a stock photo and may not match the covers of the actual item. Summary. From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations.

For modern differential geometry I cannot stress enough to study carefully the books of Jeffrey M. Lee "Manifolds and Differential Geometry" and Liviu Nicolaescu's "Geometry of Manifolds". Both are deep, readable, thorough and cover a lot of topics with a very modern style and notation.

The book is well suited for an introductory course in differential geometry, graduate students in mathematics or other sciences (physics, engineering, biology) who need to master the differential geometry of manifolds as a tool, or any mathematician who likes to read an inspiring book on the basic concepts of differential : I own a hard copy.

Despite a few typos, this is a very good book. This does for differential forms what Grinfeld did for tensors. Use it as a reference or an appetizer when reading Intro to Manifolds by Tu. This book on differential geometry by Kühnel is an excellent and useful introduction to the subject. There are many points of view in differential geometry and many paths to its concepts.

This book provides a good, often exciting and beautiful basis from which to make explorations into this deep and fundamental mathematical subject. DIFFERENTIAL GEOMETRY. Series of Lecture Notes and Workbooks for Teaching torsion, hypersurface, funda-mental forms, principal curvature, Gaussian curvature, Minkowski curvature, manifold, tensor eld, connection, geodesic curve SUMMARY: The aim of this textbook is to give an introduction to di er- di erentiable manifolds are introduced.

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra.

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory.

It presupposes little background: the reader is only expected to master basic differential calculus, and a. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus () by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced : Michael Spivak.

Introduction to Differential Geometry Lecture Notes. This note covers the following topics: Manifolds, Oriented manifolds, Compact subsets, Smooth maps, Smooth functions on manifolds, The tangent bundle, Tangent spaces, Vector field, Differential forms, Topology of manifolds, Vector bundles.

Book Overview The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different contexts.

differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a 5/5(1).

This is the third version of a book on differential manifolds. The first version appeared inand was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons.

I expanded the book inand I expand it still further today. Differential Geometry of Curves and Surfaces and Differential Geometry of Manifolds will certainly be very useful for many students.

A distinguishing feature of the books is that many of the basic notions, properties and results are illustrated by a great number of examples and figures. DIFFERENTIAL TOPOLOGY Joel W. Robbin UW Madison second author at ETH Zuric h in the spring semester of A prerequisite is the foundational chapter about smooth manifolds in [21] as well as some basic results about geodesics and the exponential map.

The rst half of this book deals with degree theory and the Pointar e{Hopf theorem File Size: 1MB. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector : Dennis Barden; Charles B Thomas.

The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds.

Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers Brand: Dover Publications. The results of Chapter V are not utilized elsewhere in this book.

It provides an introduction to the beautiful and difficult theory of foliations. These first four, or five, chapters constitute a general background not only for differential topology but also for File Size: 9MB. The course covers manifolds and differential forms for an audience of undergrad-uates who have taken a typical calculus sequence at a North American university, including basic linear algebra and multivariable calculus up to the integral theo-rems of Green, Gauss and Stokes.

With a view to the fact that vector spaces areFile Size: 2MB. About the book. Differential Geometry of Manifolds discusses the theory of differentiable and Riemannian manifolds to help students understand the basic structures and consequent developments.

Since the tangent vector plays a crucial role in the study of differentiable manifolds, this idea has been thoroughly discussed. Addeddate Identifier Hicks__Notes_on_Differential_Geometry Identifier-ark ark://t53f6rw0m Ocr ABBYY FineReader Ppi ISBN: OCLC Number: Notes: Revised edition of: Introduction to differentiable manifolds.

This book covers the following topics: Manifolds And Lie Groups, Differential Forms, Bundles And Connections, Jets And Natural Bundles, Finite Order Theorems, Methods For Finding Natural Operators, Product Preserving Functors, Prolongation Of Vector Fields And Connections, General Theory Of Lie Derivatives.

The main point of differential topology is to sort out the consequences of all this structure, and the interrelations between its various aspects.

The problem with a book about manifolds is that the basic definitions are so many, and you need them all to study their interactions with one another.

The book is well suited for an introductory course in differential geometry, graduate students in mathematics or other sciences (physics, engineering, biology) who need to master the differential geometry of manifolds as a tool, or any mathematician who likes to read an inspiring book on the basic concepts of differential geometry/5(8).

This book gives a comprehensive description of the basics of differential manifold with a full proof of any element. A large part of the book is devoted to the basic mathematical concepts in which all necessary for the development of the differential manifold is expounded and fully : World Scientific Publishing Company.

This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology.

Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and. This book has been conceived as the first volume of a tetralogy on geometry and topology.

The second volume is Differential Forms in Algebraic Topology cited above. I hope that Volume 3, Differential Geometry: Connections, Curvature, and Characteristic Classes, will soon see the light of day. Volume 4, Elements of Equiv. Lang, S., Differential and Riemannian manifolds.

Springer-Verlag, This is an updated version of Lang’s older book “Differential Manifolds”, which is one of the most commonly cited references for fundamentals in this area. The treatment is elegant and efficient. The book is well suited for an introductory course in differential geometry, graduate students in mathematics or other sciences (physics, engineering, biology) who need to master the differential geometry of manifolds as a tool, or any mathematician who likes to read an inspiring book on the basic concepts of differential geometry.The aims of this book, originally published inare to give an understanding of the basic ideas concerning stochastic differential equations on manifolds and their solution flows, to examine the properties of Brownian motion on Riemannian manifolds when it is constructed using the stochiastic development and to indicate some of the uses of the theory.

The author has. Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general.

The book provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern by:

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