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.
@article{bwmeta1.element.doi-10_2478_s11533-008-0055-3,
author = {Daniel Guan},
title = {Affine compact almost-homogeneous manifolds of cohomogeneity one},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {84-123},
zbl = {1176.53073},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0055-3}
}
Daniel Guan. Affine compact almost-homogeneous manifolds of cohomogeneity one. Open Mathematics, Tome 7 (2009) pp. 84-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0055-3/
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