Prescribing Ricci curvature on a Product of Spheres

2020/10/10 by Buttsworth, Timothy, Krishnan, Anusha M.
#53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.05118

Abstract

We prove an existence result for the prescribed Ricci curvature equation for certain doubly warped product metrics on \mathbbS^d₁+1× \mathbbS^d₂, where d_i ≥ 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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