On Jacobi-Type Vector Fields on Riemannian Manifolds

On Jacobi-Type Vector Fields on Riemannian Manifolds

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In this article, we study Jacobi-type vector fields on Riemannian manifolds.A Killing vector field is a Jacobi-type vector field while the converse is not true, leading to a natural question of finding conditions under which a Jacobi-type vector field is Killing.In this article, we first prove that every Jacobi-type vector field on tokidoki hello kitty blind box a compact Riemannian manifold is Killing.Then, we find several necessary and sufficient conditions for a Jacobi-type vector field to be a Killing vector field on non-compact Riemannian manifolds.Further, we derive some characterizations of Euclidean spaces in terms of Jacobi-type vector fields.

Finally, we 355 maybelline fit me provide examples of Jacobi-type vector fields on non-compact Riemannian manifolds, which are non-Killing.