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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  • T. Buttsworth
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2019

Riemannian Geometry

THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss's