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arXiv · 0912.0468

Geodesics on an invariant surface

Stefano Montaldo·Irene I. Onnis
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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.

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Stefano Montaldo, Irene I. Onnis. 2009-12-02. Geodesics on an invariant surface. https://arxiv.org/abs/0912.0468

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