g-natural metrics on tangent bundles and Jacobi operators
Differential Geometry
2009-12-21 v2
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.
Keywords
Cite
@article{arxiv.0907.5266,
title = {g-natural metrics on tangent bundles and Jacobi operators},
author = {S. Degla and L. Todjihounde},
journal= {arXiv preprint arXiv:0907.5266},
year = {2009}
}