Differential Forms and Applications

Manfredo P. Do Carmo

ISBN 10: 3540576185 / ISBN 13: 9783540576181

Editore: Springer Berlin Heidelberg Sep 1994, 1994

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This item is printed on demand - it takes 3-4 days longer - Neuware -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 makethem attractive to 'users' of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely the 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 R3 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. 136 pp. Englisch. Codice articolo 9783540576181

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Titolo: Differential Forms and Applications

Casa editrice: Springer Berlin Heidelberg Sep 1994

Data di pubblicazione: 1994

Legatura: Taschenbuch

Condizione: Neu

Descrizione articolo

Riassunto:

An application of differential forms for the study of 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, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

Recensione:

M.P. Do Carmo

Differential Forms and Applications

"This book treats differential forms and uses them to study some local and global aspects of differential geometry of surfaces. Each chapter is followed by interesting exercises. Thus, this is an ideal book for a one-semester course."―ACTA SCIENTIARUM MATHEMATICARUM