Affine compact almost-homogeneous manifolds of cohomogeneity one

Daniel Guan

Open Mathematics (2009)

  • Volume: 7, Issue: 1, page 84-123
  • ISSN: 2391-5455

Abstract

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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 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.

How to cite

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Daniel Guan. "Affine compact almost-homogeneous manifolds of cohomogeneity one." Open Mathematics 7.1 (2009): 84-123. <http://eudml.org/doc/269710>.

@article{DanielGuan2009,
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.},
author = {Daniel Guan},
journal = {Open Mathematics},
keywords = {Almost-homogeneous manifolds; Cohomogeneity one; Kähler-Einstein metrics; Fano manifolds; Extremal metrics; Fourth order differential equations; Fibre bundles; Existence; Futaki invariants; Geodesic stability; almost-homogeneous manifolds; cohomogeneity one; extremal metrics; fourth order differential equations; fibre bundles; existence; geodesic stability},
language = {eng},
number = {1},
pages = {84-123},
title = {Affine compact almost-homogeneous manifolds of cohomogeneity one},
url = {http://eudml.org/doc/269710},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Daniel Guan
TI - Affine compact almost-homogeneous manifolds of cohomogeneity one
JO - Open Mathematics
PY - 2009
VL - 7
IS - 1
SP - 84
EP - 123
AB - 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.
LA - eng
KW - Almost-homogeneous manifolds; Cohomogeneity one; Kähler-Einstein metrics; Fano manifolds; Extremal metrics; Fourth order differential equations; Fibre bundles; Existence; Futaki invariants; Geodesic stability; almost-homogeneous manifolds; cohomogeneity one; extremal metrics; fourth order differential equations; fibre bundles; existence; geodesic stability
UR - http://eudml.org/doc/269710
ER -

References

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