Geodesic Vector Fields on a Riemannian Manifold
Copyright policy )Geodesic Vector Fields on a Riemannian Manifold
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.
- King Saud University Saudi Arabia
- Palacký University Olomouc Czech Republic
- Palacký University, Olomouc Czech Republic
eikonal equation, Pure mathematics, geodesic vector field, QA1-939, isometric to sphere, isometric to Euclidean space, isometric to euclidean space, Mathematics
eikonal equation, Pure mathematics, geodesic vector field, QA1-939, isometric to sphere, isometric to Euclidean space, isometric to euclidean space, Mathematics
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