Fundamentals of Differential Geometry by Serge Lang

Fundamentals of Differential Geometry by Serge Lang

This text provides an introduction to basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. Although the book grew out of the author's earlier book Differential and Riemannian Manifolds, the focus has now changed from the general theory of manifolds to general differential geometry.

"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

SKU	Unavailable
ISBN 13	9780387985930
ISBN 10	038798593X
Title	Fundamentals of Differential Geometry
Author	Serge Lang
Series	Graduate Texts In Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	Springer-Verlag New York Inc.
Year published	2001-09-21
Number of pages	540
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.