Geodesic Vector Fields on a Riemannian Manifold
| Autor: | Patrik Peska, Sharief Deshmukh, Nasser Bin Turki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Geodesic
General Mathematics Acceleration (differential geometry) isometric to sphere 01 natural sciences eikonal equation 0103 physical sciences Euclidean geometry Computer Science (miscellaneous) geodesic vector field Mathematics::Metric Geometry 0101 mathematics Engineering (miscellaneous) Physics Eikonal equation lcsh:Mathematics 010102 general mathematics Mathematical analysis Zero (complex analysis) Riemannian manifold lcsh:QA1-939 Vector field 010307 mathematical physics Mathematics::Differential Geometry Unit (ring theory) isometric to euclidean space |
| Zdroj: | Mathematics, Vol 8, Iss 1, p 137 (2020) Mathematics Volume 8 Issue 1 |
| ISSN: | 2227-7390 |
| Popis: | A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to velocity. In this paper, we show that the presence of a geodesic vector field on a Riemannian manifold influences its geometry. We find characterizations of n-spheres as well as Euclidean spaces using geodesic vector fields. |
| Databáze: | OpenAIRE |
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