具有正截面曲率的$S^2 \ imes S^2$上的度量
A metric on $S^2 \times S^2$ with positive sectional curvature
AI总结：
本文构造了$S^2 \ imes S^2$上的正截面曲率度量，通过Cheeger形变得到非负曲率的Cheeger-Müter度量，再经三阶扰动得到正截面曲率度量，部分计算借助MATHEMATICA完成。
AI中文摘要：
我们构造了$S^2 \ imes S^2$上具有正截面曲率的度量。从$S^2 \ imes S^2$上的标准度量出发，我们首先进行Cheeger形变，得到的度量具有非负截面曲率，我们将其称为Cheeger-Müter度量。随后我们对该Cheeger-Müter度量进行合适的三阶扰动，并证明扰动后的度量具有正截面曲率。该证明需要大量计算，部分计算借助MATHEMATICA完成，MATHEMATICA代码已附在本次提交中。
英文摘要：
We construct a metric on $S^2 \times S^2$ with positive sectional curvature. Starting from the standard metric on $S^2 \times S^2$, we first perform a Cheeger deformation. The resulting metric has nonnegative sectional curvature. We refer to it as a Cheeger-Müter metric. We then consider a suitable third order perturbation of this Cheeger-Müter metric and show that the perturbed metrics have positive sectional curvature. The proof requires various calculations, some of which have been carried out with the help of MATHEMATICA. The MATHEMATICA code is attached to this submission.
