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Graduate Texts in Mathematics

Differential and Riemannian Manifolds

Authors: Lang, Serge

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About this Textbook

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.).

Reviews

S. Lang

Differential and Riemannian Manifolds

"An introduction to differential geometry, starting from recalling differential calculus and going through all the basic topics such as manifolds, vector bundles, vector fields, the theorem of Frobenius, Riemannian metrics and curvature. Useful to the researcher wishing to learn about infinite-dimensional geometry."

—MATHEMATICAL REVIEWS


Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4612-4182-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-0-387-94338-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4612-8688-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Differential and Riemannian Manifolds
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
160
Copyright
1995
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-4182-9
DOI
10.1007/978-1-4612-4182-9
Hardcover ISBN
978-0-387-94338-1
Softcover ISBN
978-1-4612-8688-2
Series ISSN
0072-5285
Edition Number
3
Number of Pages
XIV, 364
Additional Information
Originially published as a monograph
Topics