The Dirichlet problem for the prescribed Ricci curvature equation on cohomogeneity one manifolds

  title={The Dirichlet problem for the prescribed Ricci curvature equation on cohomogeneity one manifolds},
  author={Artem Pulemotov},
  journal={Annali di Matematica Pura ed Applicata (1923 -)},
  • Artem Pulemotov
  • Published 11 March 2013
  • Mathematics
  • Annali di Matematica Pura ed Applicata (1923 -)
Let M be a domain enclosed between two principal orbits on a cohomogeneity one manifold $$M_1$$M1. Suppose that T and R are symmetric invariant (0, 2)-tensor fields on M and $$\partial M$$∂M, respectively. The paper studies the prescribed Ricci curvature equation $${{\mathrm {Ric}}}(G)=T$$Ric(G)=T for a Riemannian metric G on M subject to the boundary condition $$G_{\partial M}=R$$G∂M=R (the notation $$G_{\partial M}$$G∂M here stands for the metric induced by G on $$\partial M$$∂M). Imposing a… 

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