Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the smooth rigidity of almost-Einstein manifolds with nonnegative
  isotropic curvature   Let $(M^n,g)$, $n \ge 4$, be a compact simply-connected Riemannian manifold
with nonnegative isotropic curvature. Given $0<l\le L$, we prove that there
exists $\eps = \eps (l,L,n)$ satisfying the following: If the scalar curvature
$s$ of $g$ satisfies $$ l \le s \le L $$ and the Einstein tensor satisfies $$ |
Ric - \frac {s}{n}g | \le \eps$$ then $M$ is diffeomorphic to a symmetric space
of compact type.
  This is a smooth analogue of the result of S. Brendle that a compact Einstein
manifold with nonnegative isotropic curvature is isometric to a locally
symmetric space.

28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn