Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flat connections, Higgs operators, and Einstein metrics on compact
  Hermitian manifolds   A flat complex vector bundle (E,D) on a compact Riemannian manifold (X,g) is
stable (resp. polystable) in the sense of Corlette [C] if it has no D-invariant
subbundle (resp. if it is the D-invariant direct sum of stable subbundles). It
has been shown in [C] that the polystability of (E,D) in this sense is
equivalent to the existence of a so-called harmonic metric in E. In this paper
we consider flat complex vector bundles on compact Hermitian manifolds (X,g).
We propose new notions of g-(poly-)stability of such bundles, and of g-Einstein
metrics in them; these notions coincide with (poly-)stability and harmonicity
in the sense of Corlette if g is a K\"ahler metric, but are different in
general. Our main result is that the g-polystability in our sense is equivalent
to the existence of a g-Hermitian-Einstein metric. Our notion of a g-Einstein
metric in a flat bundle is motivated by a correspondence between flat bundles
and Higgs bundles over compact surfaces, analogous to the correspondence in the
case of K\"ahler manifolds [S1], [S2], [S3].
  1991 Mathematics Subject Classification: 53C07

17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex