Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positively curved manifolds with large spherical rank   Rigidity results are obtained for Riemannian $d$-manifolds with $\sec
\geqslant 1$ and spherical rank at least $d-2>0$. Conjecturally, all such
manifolds are locally isometric to a round sphere or complex projective space
with the (symmetric) Fubini--Study metric. This conjecture is verified in all
odd dimensions, for metrics on $d$-spheres when $d \neq 6$, for Riemannian
manifolds satisfying the Raki\'c duality principle, and for K\"ahlerian
manifolds.

6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph