Geodesic Vector Fields on a Riemannian Manifold

Autor:	Sharief Deshmukh, Patrik Peska, Nasser Bin Turki
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	geodesic vector field eikonal equation isometric to sphere isometric to euclidean space Mathematics QA1-939
Zdroj:	Mathematics, Vol 8, Iss 1, p 137 (2020)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math8010137
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:	Directory of Open Access Journals
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