Geodésicas em superfícies

Abstract

The main objective of this monograph was to study geodesics on surfaces of revolution. We defined the concepts of covariant derivative, parallel transport, geodesic curves, the algebraic value of the covariant derivative, and geodesic curvature. We detailed the system of differential equations that determine a geodesic on a surface and calculated the geodesics for general surfaces of revolution, applying these results to the specific example of the torus through the Clairaut relation.