Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mobius fluid dynamics on the unitary groups]{M\"{o}bius fluid dynamics
  on the unitary groups   We study the nonrigid dynamics induced by the standard birational actions of
the split unitary groups $G=O_{o}\left( n,n\right) $, $SU\left( n,n\right) $
and $Sp\left( n,n\right) $ on the compact classical Lie groups $M=SO_{n}$, $%
U_{n}$ and $Sp_{n}$, respectively. More precisely, we study the geometry of $%
G$ endowed with the kinetic energy metric associated with the action of $G$ on
$M,$ assuming that $M$ carries its canonical bi-invariant Riemannian metric and
has initially a homogeneous distribution of mass. By the least action
principle, force free motions (thought of as curves in $G$) correspond to
geodesics of $G$. The geodesic equation may be understood as an inviscid
Burgers equation with M\"{o}bius constraints. We prove that the kinetic energy
metric on $G$ is not complete and in particular not invariant, find symmetries
and totally geodesic submanifolds of $G$ and address the question under which
conditions geodesics of rigid motions are geodesics of $G$. Besides, we study
equivalences with the dynamics of conformal and projective motions of the
sphere in low dimensions.

12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc