论文标题
$ k^{\ rm th} $的无限多种家庭 - 中级ricci曲率，$ k $ small
Infinite families of manifolds of positive $k^{\rm th}$-intermediate Ricci curvature with $k$ small
论文作者
论文摘要
正面$ k^{\ rm th} $ - riemannian $ n $ -manifold上的中间ricci曲率，由$ \ m mathrm {ric} _k> 0 $表示，是一种插入正分段和正面的ricci curvature（$ k = 1 $ $ k = 1 $ $ k = n-1-1）的条件。在这项工作中，我们通过检查对称和正常同质的空间以及某些脂肪均匀捆的度量，制作了许多$ \ mathrm {ric} _k> 0 $的流形的例子。结果，我们表明每个维度$ n \ geq 7 $一致，$ 3 \，\ m artrm {mod} \ 4 $支持无限的许多封闭的简单连接的成对均匀同拷贝类型的简单连接的歧管，所有这些都承认$ \ mathrm {ric} ric {ric} _k> 0 $ $ $ k <n/2 $ k <我们还证明，每个维度$ n \ geq 4 $一致性为$ 0 $或$ 1 \，\ MATHRM {mod} \ 4 $支持封闭的封闭流形，这些封闭流形带有$ \ mathrm {ric} _k> 0 $的指标，$ k \ k \ leq n/2 $，但不要接受正面的部分curvate。
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.
