Prescribing Ricci curvature on a product of spheres

@article{Buttsworth2020PrescribingRC,
  title={Prescribing Ricci curvature on a product of spheres},
  author={Timothy Buttsworth and Anusha M. Krishnan},
  journal={Annali di Matematica Pura ed Applicata (1923 -)},
  year={2020},
  volume={201},
  pages={1-36}
}
We prove an existence result for the prescribed Ricci curvature equation for certain doubly warped product metrics on $$\mathbb {S}^{d_1+1}\times \mathbb {S}^{d_2}$$ S d 1 + 1 × S d 2 , where $$d_i \ge 2$$ 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. This is the first global existence result for the prescribed Ricci curvature problem on closed cohomogeneity… 
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On the variational properties of the prescribed Ricci curvature functional
We study the prescribed Ricci curvature problem for homogeneous metrics. Given a (0,2)-tensor field T , this problem asks for solutions to the equation Ric(g) = cT for some constant c. Our approach…

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