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arXiv · 0907.5266

g-natural metrics on tangent bundles and Jacobi operators

S. Degla·L. Todjihounde
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Abstract

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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S. Degla, L. Todjihounde. 2009-12-21. g-natural metrics on tangent bundles and Jacobi operators. https://arxiv.org/abs/0907.5266

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