Geodesics on the tangent sphere bundle of 3-sphere

Abstract

The Sasaki Riemann metric g(S) on the tangent sphere bundle T1S3 of the unit 3-sphere S-3 is obtained by using the geodesic polar coordinate of S-3. The connection coefficients of the Levi Civita connection of the Sasaki Riemann manifold (T1S3, g(S)) are found. Furthermore, a system of differential equations which gives all geodesics of Sasaki Riemann manifold is obtained.