Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally Homogeneous Aspherical Sasaki Manifolds   Let $G/H$ be a contractible homogeneous Sasaki manifold. A compact locally
homogeneous aspherical Sasaki manifold $\Gamma\big\backslash G/H$ is by
definition a quotient of $G/H$ by a discrete uniform subgroup $\Gamma\leq G$.
We show that a compact locally homogeneous aspherical Sasaki manifold is always
quasi-regular, that is, $\Gamma\big\backslash G/H$ is an $S^{1}$-Seifert bundle
over a locally homogeneous aspherical K\"ahler orbifold. We discuss the
structure of the isometry group $\mathrm{Isom}(G/H)$ for a Sasaki metric of
$G/H$ in relation with the pseudo-Hermitian group $\mathrm{Psh} (G/H)$ for the
Sasaki structure of $G/H$. We show that a Sasaki Lie group $G$, when
$\Gamma\big\backslash G$ is a compact locally homogeneous aspherical Sasaki
manifold, is either the universal covering group of $SL(2,R)$ or a modification
of a Heisenberg nilpotent Lie group with its natural Sasaki structure. In
addition, we classify all aspherical Sasaki homogeneous spaces for semisimple
Lie groups.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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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: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas