Fundamentals of Differential Geometry

By: Serge Lang

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Hardcover | 30 December 1998 | Edition Number 4

At a Glance

Hardcover
564 Pages

Edition Type
Revised

Dimensions(cm)
24.0 x 16.4 x 3.6

Hardcover

$199.02

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This is the new edition of Serge Lang's "Differential and Riemannian Manifolds. " 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: for instance, the existence, uniqueness, and smoothness theorems for differential equations and the flow of a vector field; the basic theory of vector bundles including the existence of tubular neighborhoods for a submanifold; the calculus of differential forms; basic notions of symplectic manifolds, including the canonical 2-form; sprays and covariant derivatives for Riemannian and pseudo-Riemannian manifolds; applications to the exponential map, including the Cartan-Hadamard theorem and the first basic theorem of calculus of variations.

Industry 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 differential forms are expounded. The book ends with the Stokes theorem and some of its applications."-- MATHEMATICAL REVIEWS

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You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Topology Algebraic Topology Calculus & Mathematical Analysis

Foreword
Acknowledgments
General Differential Theory	p. 1
Differential Calculus	p. 3
Manifolds	p. 22
Vector Bundles	p. 43
Vector Fields and Differential Equations	p. 66
Operations on Vector Fields and Differential Forms	p. 116
The Theorem of Frobenlus	p. 155
Metrics, Covariant Derivatives, and Riemannian Geometry	p. 171
Metrics	p. 173
Covariant Derivatives and Geodesics	p. 196
Curvature	p. 231
Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle	p. 267
Curvature and the Variation Formula	p. 294
An Example of Seminegative Curvature	p. 322
Automorphisms and Symmetries	p. 339
Immersions and Submersions	p. 369
Volume Forms and Integration	p. 395
Volume Forms	p. 397
Integration of Differential Forms	p. 448
Stokes' Theorem	p. 475
Applications of Stokes' Theorem	p. 489
The Spectral Theorem	p. 511
Bibliography	p. 523
Index	p. 531
Table of Contents provided by Blackwell. All Rights Reserved.

Fundamentals of Differential Geometry

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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