Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifolds with nonnegative isotropic curvature   We prove that if $(M^n,g)$, $n \ge 4$, is a compact, orientable, locally
irreducible Riemannian manifold with nonnegative isotropic curvature, then one
of the following possibilities hold:
  (i) $M$ admits a metric with positive isotropic curvature
  (ii) $(M,g)$ is isometric to a locally symmetric space
  (iii) $(M,g)$ is K\"ahler and biholomorphic to $\C P^\frac {n}{2}$.
  (iv) $(M,g)$ is quaternionic-K\"ahler.
  This is implied by the following result:
  Let $(M^{2n},g)$ be a compact, locally irreducible K\"ahler manifold with
nonnegative isotropic curvature. Then either $M$ is biholomorphic to $\C P^n$
or isometric to a compact Hermitian symmetric space. This answers a question of
Micallef and Wang in the affirmative.
  The proof is based on the recent work of S. Brendle and R. Schoen on the
Ricci flow.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ