Displaying similar documents to “Rigidity of homogeneous contact manifolds under Fano deformation.”

Affine compact almost-homogeneous manifolds of cohomogeneity one

Daniel Guan (2009)

Open Mathematics

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This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to...