Abstract
We consider the existence of Calabi extremal metrics on certain compact almost homogeneous manifold of cohomogeneity one. We proved that the positivity of the generalized Futaki invariant implies the existence. We expect that the converse is also true for all this kind of manifolds.
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Guan, D. Existence of extremal metrics on almost homogeneous manifolds of cohomogeneity one—II. J Geom Anal 12, 63–79 (2002). https://doi.org/10.1007/BF02930860
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DOI: https://doi.org/10.1007/BF02930860