One of the main goals of this project is to study the index of vector fields in compact surfaces and present the Poincar´e-Hopf Theorem, remarking that such a result connects topological elements to geometric objects.

In this work, we study the concepts of degree and local degree for maps between manifolds. Furthermore, we define the Poincaré-Hopf index and study some relevant proprieties of this index such as the famous Poincaré-Hopf ...

Desde o surgimento da definição de superfícies parametrizadas, foi questionado sobre suas propriedades que independem da parametrização. Propriedades essas que caracterizam objetivamente a geometria dessa família facilitando ...

In this work, we present a study on the theory of differential geometry of surfaces with a language of moving references. At first, we will introduce some groups of matrices and their actions in Euclidean space. Once this ...

The Lebesgue measure is an important concept with applications in the Lebesgue integral, in the axiomatization of probabilities, and in the definion of integral of spaces more general than the euclidian spaces. This essay ...