Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An invariant K\"ahler metric on the tangent disk bundle of a space-form   We find a family of K\"ahler metrics invariantly defined on the radius
$r_0>0$ tangent disk bundle ${{\cal T}_{M,r_0}}$ of any given real space-form
$M$ or any of its quotients by discrete groups of isometries. Such metrics are
complete in the non-negative curvature case and non-complete in the negative
curvature case. If $\dim M=2$ and $M$ has constant sectional curvature
$K\neq0$, then the K\"ahler manifolds ${{\cal T}_{M,r_0}}$ have holonomy
$\mathrm{SU}(2)$; hence they are Ricci-flat. For $M=S^2$, just this dimension,
the metric coincides with the Stenzel metric on the tangent manifold ${{\cal
T}_{S^2}}$, giving us a new most natural description of this well-know metric.

24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex