Geodesics on an invariant surface

2009/12/02 by Stefano Montaldo, Montaldo, Stefano, Irene I. Onnis +1
Mathematics · Physics and Astronomy · #53B15 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.DG #msc:53B15 #msc:53C42

paper · pdf · doi:10.48550/arxiv.0912.0468

14 pages, 1 figure

arxiv created 2009/12/02 · openalex publication_date 2009/12/02 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Invariant surfaces in homogenous space Sol with constant curvature

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