标题： 某些乘积流形上的非负曲率 显示英文标题

标题： Non-negative curvature on certain product manifolds

摘要： 设$G/H$为一个闭的、单连通的齐性流形。 假设在$G/H$上所有实向量丛的稳定类中都包含一个齐性丛。 那么，对于任何与$G/H$同伦等价的闭的、单连通的光滑流形$M$，存在$n>\mathrm{dim}(M)$使得乘积流形 $M\times S^{n}$具有一个非负截面曲率的度量。 许多齐性流形满足这个假设，包括单连通紧致的一阶对称空间，以及其他一些例子。 显示英文摘要

摘要： Let $G/H$ be a closed, simply connected homogeneous manifold. Suppose every stable class of real vector bundles over $G/H$ contains a homogeneous bundle. Then, for any closed, simply connected smooth manifold $M$ homotopy equivalent to $G/H$, there exists $n>\mathrm{dim}(M)$ such that the product manifold $M\times S^{n}$ admits a metric with non-negative sectional curvature. Many homogeneous manifolds satisfy this assumption, including simply connected compact rank-one symmetric spaces, and among others.