Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On complete hyperK\"ahler manifolds with compact isometry group   The basic model of hyperK\"ahler manifold is the quaternionic number space
$\HH^n$ with flat and symmetric metric. In this note we shall construct a
one-parameter family of complete hyperK\"ahler metrics on $\HH^n$ whose
isometry group is the compact group ${\rm Sp}(n)\cdot{\rm Sp}(1)$. The standard
\emph{quaternionic Carnot-Carath\'eodory structure} on the $4n+3$-dimensional
quaternionic Heisenberg Lie group $\cM$ induces the standard hyperK\"ahler
structure on the base $\HH^n$. By deforming a Carnot-Carath\'eodory structure
on $\cM$, the resulting Hermitian metric on $\HH^n$ is shown to be
\emph{complete hyperK\"ahler}.

7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom