Geodesics on an invariant surface
classification
🧮 math.DG
keywords
geodesicsinvariantsurfacedescriptiondimensionalgeodesicthreecharacterization
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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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