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

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Abstract

Consider a compact Lie group G and a closed Lie subgroup \(H<G\). Let \({\mathcal {M}}\) be the set of G-invariant Riemannian metrics on the homogeneous space \(M=G/H\). By studying variational properties of the scalar curvature functional on \({\mathcal {M}}\), 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 generalised flag manifold.

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Acknowledgements

I am grateful to Andreas Arvanitoyeorgos and Marina Statha for suggesting that I consider the prescribed Ricci curvature problem on generalised Wallach spaces.

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  1. School of Mathematics and Physics, The University of Queensland, St Lucia, QLD, 4072, Australia

    Artem Pulemotov

  2. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Artem Pulemotov

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  1. Artem Pulemotov
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Correspondence to Artem Pulemotov.

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Artem Pulemotov’s research is supported under the Australian Research Council’s Discovery Projects funding scheme (DP180102185).

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Pulemotov, A. Maxima of Curvature Functionals and the Prescribed Ricci Curvature Problem on Homogeneous Spaces. J Geom Anal 30, 987–1010 (2020). https://doi.org/10.1007/s12220-019-00175-6

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  • DOI: https://doi.org/10.1007/s12220-019-00175-6

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