Differential forms and applications
By: Manfredo P. do Carmo.
Series: Universitext
Publisher: Springer-Verlag
Published: 1994
Place of publication: Berlin; New York
Language: eng
Number of pages: 118
Subjects: Differential forms
Description: The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem of differential forms, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames of E.

Cartan to study the local differential geometry of immersed surfaces in R[superscript 3] as well as the intrinsic geometry of surfaces. Everything is then put together in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.
Notes: Includes bibliographical references (p. [115]) and index.