Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous Nonrelativistic Geometries as Coset Spaces   We generalize the coset procedure of homogeneous spacetimes in
(pseudo-)Riemannian geometry to non-Lorentzian geometries. These are manifolds
endowed with nowhere vanishing invertible vielbeins that transform under local
non-Lorentzian tangent space transformations. In particular, we focus on
nonrelativistic symmetry algebras that give rise to (torsional) Newton-Cartan
geometries, for which we demonstrate how the Newton-Cartan metric complex is
determined by degenerate co- and contravariant symmetric bilinear forms on the
coset. In specific cases, we also show the connection of the resulting
nonrelativistic coset spacetimes to pseudo-Riemannian cosets via
In\"on\"u-Wigner contraction of relativistic algebras as well as null
reduction. Our construction is of use for example when considering limits of
the AdS/CFT correspondence in which nonrelativistic spacetimes appear as
gravitational backgrounds for nonrelativistic string or gravity theories.

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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas