English

Geodesics on an invariant surface

Differential Geometry 2009-12-03 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0912.0468,
  title  = {Geodesics on an invariant surface},
  author = {Stefano Montaldo and Irene I. Onnis},
  journal= {arXiv preprint arXiv:0912.0468},
  year   = {2009}
}

Comments

14 pages, 1 figure

R2 v1 2026-06-21T14:18:47.847Z