Classification of compact homogeneous spaces with invariant symplectic structures.
Classification of compact complex homogeneous spaces with invariant volumes.
Examples of compact holomorphic symplectic mainfolds which are not Kählerian II.
On representation theory and the cohomology rings of irreducible compact hyperkähler manifolds of complex dimension four
In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.
Affine compact almost-homogeneous manifolds of cohomogeneity one
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...
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