MATVEEV, Vladimir; MOUNOUD, Pierre

doi:10.1007/s10455-010-9211-7

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MATVEEV, Vladimir
Mathematisches Institut, FSU Jena

MOUNOUD, Pierre
Institut de Mathématiques de Bordeaux [IMB]

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Annals of Global Analysis and Geometry. 2010, vol. 38, n° 3, p. 259-271

Springer Verlag

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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 Levi-Civita 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 $(O(p+1,q),S^{p,q})$-manifold does not preserve any nondegenerate splitting of $\R^{p+1,q}$.< Leer menos

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

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