Overview
- New edition of a successful Serge Lang title
- Written in the authors unique and engaging style, with clear and elegant proofs
- Covers the fundamentals of differential geometry, differential topology, and differential equations
- Includes new chapters on Jacobi lifts, tensorial splitting of the double tangent bundle, curvature and the variation formula, and an example of semi-negative curvature
- New chapters, sections, examples, and exercises have been added
Part of the book series: Graduate Texts in Mathematics (GTM, volume 191)
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Table of contents (18 chapters)
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General Differential Theory
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Metrics, Covariant Derivatives, and Riemannian Geometry
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Volume Forms and Integration
Reviews
"There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books. ...
It can be warmly recommended to a wide audience."
EMS Newsletter, Issue 41, September 2001
"The text provides a valuable introduction to basic concepts and fundamental results in differential geometry. A special feature of the book is that it deals with infinite-dimensional manifolds, modeled on a Banach space in general, and a Hilbert space for Riemannian geometry. The set-up works well on basic theorems such as the existence, uniqueness and smoothness theorem for differential equations and the flow of a vector field, existence of tubular neighborhoods for a submanifold, and the Cartan-Hadamard theorem. A major exception is the Hopf-Rinow theorem. Curvature and basic comparison theorems are discussed. In the finite-dimensional case, volume forms, the Hodge star operator, and integration of differentialforms are expounded. The book ends with the Stokes theorem and some of its applications."-- MATHEMATICAL REVIEWS
Authors and Affiliations
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Bibliographic Information
Book Title: Fundamentals of Differential Geometry
Authors: Serge Lang
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-0541-8
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1999
Hardcover ISBN: 978-0-387-98593-0Published: 30 December 1998
Softcover ISBN: 978-1-4612-6810-9Published: 05 October 2012
eBook ISBN: 978-1-4612-0541-8Published: 06 December 2012
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVII, 540
Topics: Algebraic Topology, Analysis