Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds
  and applications   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
$\R^{p+1,q}$.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph