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Differential Forms and Applications
English
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§Dieses Buch vom M. do Carmo, Träger des Mathematikpreises 1992 der "Third World Academy of Sciences", gibt eine Einführung in die Theorie differenzierbarer Formen. Da es nur Grundkenntnisse in Differential- und Integralrechnung sowie linearer Algebra voraussetzt, eignet es sich als Lehrbuch für Mathematik- und Physikstudenten im 4.- 6. Semester. 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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