An Introduction to Differentiable Manifolds and Riemannian Geometry
Title | An Introduction to Differentiable Manifolds and Riemannian Geometry PDF eBook |
Author | |
Publisher | Academic Press |
Pages | 441 |
Release | 1975-08-22 |
Genre | Mathematics |
ISBN | 0080873790 |
An Introduction to Differentiable Manifolds and Riemannian Geometry
An Introduction to Differentiable Manifolds and Riemannian Geometry
Title | An Introduction to Differentiable Manifolds and Riemannian Geometry PDF eBook |
Author | |
Publisher | Academic Press |
Pages | 447 |
Release | 1986-04-21 |
Genre | Mathematics |
ISBN | 0080874398 |
An Introduction to Differentiable Manifolds and Riemannian Geometry
An Introduction to Differential Manifolds
Title | An Introduction to Differential Manifolds PDF eBook |
Author | Jacques Lafontaine |
Publisher | Springer |
Pages | 408 |
Release | 2015-07-29 |
Genre | Mathematics |
ISBN | 3319207350 |
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 little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.
Introduction to Riemannian Manifolds
Title | Introduction to Riemannian Manifolds PDF eBook |
Author | John M. Lee |
Publisher | Springer |
Pages | 447 |
Release | 2019-01-02 |
Genre | Mathematics |
ISBN | 3319917552 |
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Differential and Riemannian Manifolds
Title | Differential and Riemannian Manifolds PDF eBook |
Author | Serge Lang |
Publisher | Springer Science & Business Media |
Pages | 376 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461241820 |
This is the third version of a book on differential manifolds. The first version appeared in 1962, and 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 in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).
Manifolds and Differential Geometry
Title | Manifolds and Differential Geometry PDF eBook |
Author | Jeffrey Marc Lee |
Publisher | American Mathematical Soc. |
Pages | 690 |
Release | 2009 |
Genre | Mathematics |
ISBN | 0821848151 |
Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.
Riemannian Manifolds
Title | Riemannian Manifolds PDF eBook |
Author | John M. Lee |
Publisher | Springer Science & Business Media |
Pages | 232 |
Release | 2006-04-06 |
Genre | Mathematics |
ISBN | 0387227261 |
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.