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arXiv · 2010.05118

Prescribing Ricci curvature on a Product of Spheres

Timothy Buttsworth·Anusha M. Krishnan
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Abstract

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.

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Timothy Buttsworth, Anusha M. Krishnan. 2020-10-10. Prescribing Ricci curvature on a Product of Spheres. https://arxiv.org/abs/2010.05118

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