Riemannian and Sub-Riemannian Geodesic Flows
| Autor: | Mauricio Godoy Molina, Erlend Grong |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Geodesic Riemannian submersion 010102 general mathematics Mathematical analysis Geodesic map Fundamental theorem of Riemannian geometry Riemannian geometry 01 natural sciences Levi-Civita connection 53C17 53C22 53C12 symbols.namesake Differential Geometry (math.DG) 0103 physical sciences FOS: Mathematics symbols Mathematics::Metric Geometry Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Exponential map (Riemannian geometry) Solving the geodesic equations Mathematics |
| Zdroj: | The Journal of Geometric Analysis. 27:1260-1273 |
| ISSN: | 1559-002X 1050-6926 |
| DOI: | 10.1007/s12220-016-9717-8 |
| Popis: | In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of sub-Riemannian metrics on totally geodesic Riemannian submersions. As a consequence we can characterize sub-Riemannian geodesics as the horizontal lifts of projections of Riemannian geodesics. 12 pages |
| Databáze: | OpenAIRE |
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