We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are the characterization of geodesic orbits, Clairaut’s relation and its geometric interpretation in some remarkable three dimensional spaces, the local description of the geodesics, and the explicit description of geodesic curves on an invariant surface with constant Gauss curvature.
Geodesic on a invariant surface
MONTALDO, STEFANO;ONNIS I. I.
2011-01-01
Abstract
We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are the characterization of geodesic orbits, Clairaut’s relation and its geometric interpretation in some remarkable three dimensional spaces, the local description of the geodesics, and the explicit description of geodesic curves on an invariant surface with constant Gauss curvature.
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