Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local and global rigidity for isometric actions of simple Lie groups on
  pseudo-Riemannian manifolds   Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an
isometric $G$-action with a dense orbit, where $G$ is a connected non-compact
simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the
normal bundle to the $G$-orbits is non-integrable and for suitable conditions,
we prove that $M$ has a $G$-invariant metric which is locally isometric to a
Lie group with a bi-invariant metric (local rigidity theorem). The latter does
not require $M$ to be complete as in previous works. We also prove a general
result showing that $M$ is, up to a finite covering, of the form $H/\Gamma$
($\Gamma$ a lattice in the group $H$) when we assume that $M$ is complete
(global rigidity theorem). For both the local and the global rigidity theorems
we provide cases that imply the rigidity of $G$-actions for $G$ given by
$\mathrm{SO}_0(p,q)$, $G_{2(2)}$ or a non-compact simple Lie group of type
$F_4$ over $\mathbb{R}$. We also survey the techniques and results related to
this work.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph