g-natural metrics on tangent bundles and Jacobi operators

Details g-natural metrics on tangent bundles and Jacobi operators g-natural metrics on tangent bundles and Jacobi operators

2009-07-30

arxiv.org/abs/0907.5266v2

Mathematics

Differential Geometry

Scientific paper

Let (M,g) be a Riemannian manifold and G a nondegenerate g-natural metric on its tangent bundle T M . In this paper we establish a relation between the Jacobi operators of (M,g) and that of (T M,G). In the case of a Riemannian surface (M,g), we compute explicitly the spectrum of some Jacobi operators of (TM,G) and give necessary and sufficient conditions for (T M,G) to be an Osserman manifold.

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