Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with
  transverse symmetries   We prove a lower bound for the first eigenvalue of the sub-Laplacian on
sub-Riemannian manifolds with transverse symmetries. When the manifold is of
H-type, we obtain a corresponding rigidity result: If the optimal lower bound
for the first eigenvalue is reached, then the manifold is equivalent to a 1 or
a 3-Sasakian sphere.

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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph