Maxima of Curvature Functionals and the Prescribed Ricci Curvature Problem on Homogeneous Spaces

@article{Pulemotov2019MaximaOC,
  title={Maxima of Curvature Functionals and the Prescribed Ricci Curvature Problem on Homogeneous Spaces},
  author={Artem Pulemotov},
  journal={The Journal of Geometric Analysis},
  year={2019},
  volume={30},
  pages={987-1010}
}
  • A. Pulemotov
  • Published 4 January 2016
  • Mathematics
  • The Journal of Geometric Analysis
Consider a compact Lie group G and a closed Lie subgroup $$H<G$$ H < G . Let $${\mathcal {M}}$$ M be the set of G -invariant Riemannian metrics on the homogeneous space $$M=G/H$$ M = G / H . By studying variational properties of the scalar curvature functional on $${\mathcal {M}}$$ M , we obtain an existence theorem for solutions to the prescribed Ricci curvature problem on  M . To illustrate the applicability of this result, we explore cases where M is a generalised Wallach space and a… 

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