Affine compact almost-homogeneous manifolds of cohomogeneity one

• Autorzy: Daniel Guan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Almost-homogeneous manifolds; Cohomogeneity one; Kähler-Einstein metrics; Fano manifolds; Extremal metrics; Fourth order differential equations; Fibre bundles; Existence; Futaki invariants; Geodesic stability

Kategorie tematyczne

• 53C10: G -structures
• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 32L05: Holomorphic bundles and generalizations
• 53C55: Hermitian and K\"ahlerian manifolds
• 32Q20: K\"ahler-Einstein manifolds
• 32M12: Almost homogeneous manifolds and spaces
• 14M17: Homogeneous spaces and generalizations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 1
• Strony: 84-123

Daty

wydano

2009-03-01

online

2009-01-10

Twórcy

autor

Daniel Guan

• Department of Mathematics, University of California at Riverside, California, USA

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-008-0055-3