A aplicação normal de Gauss: classificação de pontos em superfícies.

Abstract

The Normal Application of Gauss presents a fundamental theory in the study of regular surfaces, because through this linear application we can obtain numerous property of surfaces in a neighborhood of any point p. With the application of Gauss is it possible to measure how quickly a regular surface S moves away from its tangent plane TpS , in the vicinity of a point on this surface. With the derivative of N, dNP, it will be possible to measure how far N moves away from N(p) in a neighborhood of p. It is differential is a self-adjoint linear application, and will serve to present the second fundamental form he S in p. We will use the Normal Gauss Application for the study of the Gaussian and Average curvatures of some regular surfaces, and the classification of points of such surfaces.