Primeiro autovalor do Laplaciano: aspectos analíticos e geométricos

Abstract

The notion of differentiable manifold is a concept similar to the regular surface, however, is an intrinsic notion, and therefore need not be contained in a Euclidean space. The first eigenvalue of the Laplacian, an elliptic differential operator of second order is an analytic entity that will be used to provide geometrical information about a submanifold isometrically immersed in Euclidean space. In this dissertation, will be presented the basic notions of Riemannian Geometry such as Differentiable Manifolds, Tangent Spaces, Riemannian Manifolds, Affine Connections, Curvatures and Isometric Immersions