
Fundamentals of Differential Geometry
Serge Lang(Author)
Springer (Publisher)
1st Edition
Published on 5. October 2012
Book
Paperback/Softback
XVII, 540 pages
978-1-4612-6810-9 (ISBN)
Description
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises.
From the 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." --EMS NEWSLETTER
From the 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." --EMS NEWSLETTER
Reviews / Votes
"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 REVIEWSMore details
Product info
Paperback
Series
Band 191
Language
English
Place of publication
New York, NY
United States
Target group
Graduate
Product notice
Paperback (trade)
Illustrations
biography
Dimensions
Height: 236 mm
Width: 154 mm
Thickness: 32 mm
Weight
841 gr
ISBN-13
978-1-4612-6810-9 (9781461268109)
DOI
10.1007/978-1-4612-0541-8
Schweitzer Classification
Other editions
Additional editions


Serge Lang
Fundamentals of Differential Geometry
Book
09/2001
1st Edition
Springer
€106.99
Shipment within 5-7 days
Content
I: GENERAL DIFFERENTIAL THEORY. 1: Differential Calculus. 2: Manifolds. 3: Vector Bundles. 4: Vector Fields and Differential Equations. 5: Operations on Vector Fields and Differential Forms. 6: The Theorem of Frobenius. II: METRICS, COVARIANT DERIVATIVES AND RIEMANNIAN GEOMETRY. 7: Metrics. 8: Covariant Derivatives and Geodesics. 9: Curvature. 10: Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle. 11: Curvature and the Variation Formula. 12: An Example of Seminegative Curvature. 13: Automorphisms and Symmetries. III: VOLUME FORMS AND INTEGRATION. 15: Volume Forms. 16: Integration of Differential Forms. 17: Stokes' Theorem. 18: Applications of Stokes' Theorem. Appendix: The Spectral Theorem.