Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On globally hypoelliptic abelian actions and their existence on
  homogeneous spaces   We define globally hypoelliptic smooth $\mathbb R^k$ actions as actions whose
leafwise Laplacian along the orbit foliation is a globally hypoelliptic
differential operator. When $k=1$, strong global rigidity is conjectured for
such actions by Greenfield-Wallach and Katok: every such action is smoothly
conjugate to a Diophantine flow on the torus. The conjecture has been confirmed
for all homogeneous flows on homogeneous spaces \cite{FFRH}. In this paper we
conjecture that among homogeneous $\mathbb R^k$ actions ($k\ge 2$) on
homogeneous spaces globally hypoelliptic actions exist only on nilmanifolds. We
obtain a partial result towards this conjecture: we show non-existence of
globally hypoelliptic $\mathbb R^2$ actions on homogeneous spaces $G/\Gamma$,
with at least one quasi-unipotent generator, where $G= SL(n, \mathbb R)$. We
also show that the same type of actions on solvmanifolds are smoothly conjugate
to homogeneous actions on nilmanifolds.

35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio