Geodesics on an invariant surface

Details Geodesics on an invariant surface Geodesics on an invariant surface

2009-12-02

arxiv.org/abs/0912.0468v1

Mathematics

Differential Geometry

14 pages, 1 figure

Scientific paper

We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are: the characterization of geodesic orbits; a Clairaut's relation and its geometric interpretation in some remarkable three dimensional spaces; the local description of the geodesics; the explicit description of geodesic curves on an invariant surface with constant Gauss curvature.

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