Affine compact almost-homogeneous manifolds of cohomogeneity one
Copyright policy )Affine compact almost-homogeneous manifolds of cohomogeneity one
Abstract 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 the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.
- University of California, Riverside United States
Almost homogeneous manifolds and spaces, Fano manifolds, Global differential geometry of Hermitian and Kählerian manifolds, 53c10, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, 53c55, Kähler-Einstein metrics, futaki invariants, 32q20, QA1-939, 32l05, fourth order differential equations, 14m17, kähler-einstein metrics, Homogeneous spaces and generalizations, Kähler-Einstein manifolds, fibre bundles, existence, 53c21, fano manifolds, extremal metrics, almost-homogeneous manifolds, cohomogeneity one, 32m12, Holomorphic bundles and generalizations, Futaki invariants, geodesic stability, Mathematics
Almost homogeneous manifolds and spaces, Fano manifolds, Global differential geometry of Hermitian and Kählerian manifolds, 53c10, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, 53c55, Kähler-Einstein metrics, futaki invariants, 32q20, QA1-939, 32l05, fourth order differential equations, 14m17, kähler-einstein metrics, Homogeneous spaces and generalizations, Kähler-Einstein manifolds, fibre bundles, existence, 53c21, fano manifolds, extremal metrics, almost-homogeneous manifolds, cohomogeneity one, 32m12, Holomorphic bundles and generalizations, Futaki invariants, geodesic stability, Mathematics
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