Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite families of manifolds of positive $k^{\rm th}$-intermediate
  Ricci curvature with $k$ small   Positive $k^{\rm th}$-intermediate Ricci curvature on a Riemannian
$n$-manifold, to be denoted by $\mathrm{Ric}_k > 0$, is a condition that
interpolates between positive sectional and positive Ricci curvature (when $k
=1$ and $k=n-1$ respectively). In this work, we produce many examples of
manifolds of $\mathrm{Ric}_k > 0$ with $k$ small by examining symmetric and
normal homogeneous spaces, along with certain metric deformations of fat
homogeneous bundles. As a consequence, we show that every dimension $n\geq 7$
congruent to $3\,\mathrm{mod}\ 4$ supports infinitely many closed simply
connected manifolds of pairwise distinct homotopy type, all of which admit
homogeneous metrics of $\mathrm{Ric}_k > 0$ for some $k<n/2$. We also prove
that each dimension $n\geq 4$ congruent to $0$ or $1\,\mathrm{mod}\ 4$ supports
closed manifolds which carry metrics of $\mathrm{Ric}_k > 0$ with $k\leq n/2$,
but do not admit metrics of positive sectional curvature.

30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
19
The categories of this paper are: eess
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn