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Introduction to differential forms and applications

Grant number: 14/19034-5
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): December 01, 2014
Effective date (End): November 30, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Glaucio Terra
Grantee:Rodrigo Rey Carvalho
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Our aim is to study differential forms in Differential Geometry and applications. We shall consider vector-valued differential forms (taking values on Banach spaces) defined on open subsets of Banach spaces or finite dimensional differentiable manifolds. The applications to be considered are: 1) elementary theory of analytic functions of one complex variable by means of a differential forms approach; 2) Cartan method of the moving frame and applications in Differential Geometry, such as Gauss-Bonnet and Morse theorems in the context of embedded surfaces in R3; 3) geometric version of local Frobenius theorem for total differential equations, using differential forms.The student is expected to contribute with his own ideas and proofs.