Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of a complete holomorphic vector field via the
  K\"ahler-Einstein metric   In this paper, we study the existence of a complete holomorphic vector fields
on a strongly pseudoconvex complex manifold admitting a negatively curved
complete K\"ahler-Einstein metric and a discrete sequence of automorphisms.
Using the method of potential scaling, we will show that there is a potential
function of the K\"ahler-Einstein metric whose differential has a constant
length. Then we will construct a complete holomorphic vector field from the
gradient vector field of the potential function.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph