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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access January 10, 2009

Affine compact almost-homogeneous manifolds of cohomogeneity one

Daniel Guan
From the journal Open Mathematics

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.

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Published Online: 2009-1-10
Published in Print: 2009-3-1

© 2009 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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