Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of approximate Hermitian-Einstein structures on semistable
  principal bundles   Let E_G be a principal G-bundle over a compact connected K\"ahler manifold,
where G is a connected reductive complex linear algebraic group. We show that
E_G is semistable if and only if it admits approximate Hermitian-Einstein
structures.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph