Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application
Differential Geometry
2009-07-13 v1
Abstract
In this article we extend the Gallot-Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over such a manifold admits a parallel symmetric 2-tensor then it is incomplete and has non zero constant curvature. An application of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics is given.
Keywords
Cite
@article{arxiv.0907.1889,
title = {Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application},
author = {Pierre Mounoud},
journal= {arXiv preprint arXiv:0907.1889},
year = {2009}
}