Geodesic Vector Fields on a Riemannian Manifold

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 veloci...

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Bibliographic Details
Main Authors: Sharief Deshmukh, Patrik Peska, Nasser Bin Turki
Format: Article
Language:English
Published: MDPI AG 2020-01-01
Series:Mathematics
Subjects:
geodesic vector field
eikonal equation
isometric to sphere
isometric to euclidean space
Online Access:https://www.mdpi.com/2227-7390/8/1/137
Description
Summary: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 <i>n</i>-spheres as well as Euclidean spaces using geodesic vector fields.
ISSN:2227-7390

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