Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive Complex Sectional Curvature, Ricci Flow and the Differential
  Sphere Theorem   The paper provides a different proof of the result of Brendle-Schoen on the
differential sphere theorem. It is shown directly that the invariant cone of
curvature operators with positive (or non-negative) complex sectional curvature
is preserved by the Ricci flow. This implies, by a result of B\"ohm-Wilking,
that the normalized Ricci flow deforms such a metric to a metric of constant
positive curvature. Using earlier work of Yau and Zheng it can be shown that a
metric with strictly (pointwise) 1/4-pinched sectional curvature has positive
complex sectional curvature. This gives a direct proof of Brendle-Schoen's
recent differential sphere theorem, bypassing any discussion of positive
isotropic curvature.

24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph