Primeira forma fundamental e aplicações

Abstract

The present work discusses the first fundamental, or quadratic, form of a surface. This is a geometric structure through which we obtain measurements of curve length, angle, and area of regions of a surface. For this task, we consider the tangent plane, and at each point of it, we calculate the inner product. As a result, and through the first quadratic form, we can determine the said geometric aspects having as the only possible way the own surface, in other words, disregarding the ambient space. In this study we will apply the first fundamental form in order to demonstrate and exemplify such properties, as well as its usefulness and importance for math.