Автор: Manfredo P. Do Carmo
Название: Differential Forms and Applications
Издательство: Springer
Год: 1994
ISBN: 0387576185
Серия: Universitext
Язык: English
Формат: pdf
Размер: 0,6 mb
Страниц: 126
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.