Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Generalisation of Obata's theorem   In a complete Riemannian manifold $(M, g)$ if the hessian of a real valued
function satisfies some suitable conditions then it restricts the geometry of
$(M, g)$. In this paper we characterize all compact rank-1 symmetric spaces, as
those Riemannian manifolds $(M, g)$ admitting a real valued function $u$ such
that the hessian of $u$ has atmost two eigenvalues $-u$ and $-{{u+1}\over 2}$,
under some mild hypothesis on $(M, g)$. This generalises a well known result of
Obata which characterizes all round spheres.

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The categories of this paper are: hep-th
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The categories of this paper are: physics
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th