Geodesic Vector Fields on a Riemannian Manifold

Sharief Deshmukh, Patrik Peska and Nasser Bin Turki
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Sharief Deshmukh: Department of Mathematics, College of science, King Saud University, P.O. Box-2455 Riyadh 11451, Saudi Arabia
Patrik Peska: Department of Algebra and Geometry, Palacky University, 77146 Olomouc, Czech Republic
Nasser Bin Turki: Department of Mathematics, College of science, King Saud University, P.O. Box-2455 Riyadh 11451, Saudi Arabia

Mathematics, 2020, vol. 8, issue 1, 1-11

Abstract: 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.

Keywords: geodesic vector field; eikonal equation; isometric to sphere; isometric to Euclidean space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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