Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application

Details Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application

2009-07-10

arxiv.org/abs/0907.1889v1

Mathematics

Differential Geometry

Scientific paper

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.

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