On Geodesics of 3D Surfaces of Rotations in Euclidean and Minkowskian Spaces

Anis I. Saad, Saif Alislam E. Muhammed, Tarig S. Elmabrouk

In this paper we review geodesics on  surfaces of revolution in classical differential geometry, and prove the  analogous result in three-dimensional Minowski space; which does have three types of surfaces of rotations [9]. So there are three types of geodesics on those surfaces.  Then we introduce some examples explicitly in both cases; the usual one which Euclidean space and the cases of Minkowskian spaces considering a time-like geodesic. And then we visualize some geodesics on those surfaces using Maple. Which showing how the Euclidean and Minkowskian geodesics are differ.