Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications

@inproceedings{Matveev2009GallotTannoTF,
  title={Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications},
  author={Vladimir S. Matveev and Pierre Mounoud},
  year={2009}
}
We extend the Gallot-Tanno Theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric (0, 2)−tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct LeviCivita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed (O(p + 1, q), S)-manifold does not preserve any… CONTINUE READING

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