Article ID Journal Published Year Pages File Type
1896316 Journal of Geometry and Physics 2011 6 Pages PDF
Abstract

In this paper, we use a Killing vector field on a Riemannian manifold to characterize odd-dimensional spheres and Einstein manifolds.

► An important question in geometry of a Riemannian manifold is to characterize Einstein manifolds. ► We use a Killing vector field to characterize Einstein manifolds. ► A necessary condition for a Riemannian manifold to be isometric to an Odd-dimensional sphere is obtained using a Killing vector field. ► A characterization of the Euclidean space is found using Killing vector fields.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
Authors
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