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, 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.
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Text: English (translation)
Original Language: Portugese
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
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Descripción Springer. Estado de conservación: New. Nº de ref. de la librería 8183012
Descripción Springer, 1997. Paperback. Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería DADAX0387576185
Descripción Springer, 1994. Paperback. Estado de conservación: New. Never used!. Nº de ref. de la librería P110387576185