论文标题
在球体的产物上开处方RICCI曲率
Prescribing Ricci curvature on a Product of Spheres
论文作者
论文摘要
我们证明了在$ \ Mathbb {s}^{d_1+1} \ times \ times \ Mathbb {s}^{d_2} $上，在$ \ mathbb {s}^{s}^{d_1+1}^$上，在其中$ d_i \ geq 2 $。如果$ t $是满足某些曲率假设的度量，我们表明$ t $可以独立于这两个因素上缩放，以便本身是某些度量标准的Ricci张量。
We prove an existence result for the prescribed Ricci curvature equation for certain doubly warped product metrics on $\mathbb{S}^{d_1+1}\times \mathbb{S}^{d_2}$, where $d_i \geq 2$. If $T$ is a metric satisfying certain curvature assumptions, we show that $T$ can be scaled independently on the two factors so as to itself be the Ricci tensor of some metric.
