An obstruction to homogeneous manifolds being Kähler

@article{Gilligan2005AnOT,
  title={An obstruction to homogeneous manifolds being K{\"a}hler},
  author={B Gilligan},
  journal={Annales de l'Institut Fourier},
  year={2005},
  volume={55},
  pages={229-241}
}
  • B. Gilligan
  • Published 2005
  • Mathematics
  • Annales de l'Institut Fourier
Soit G un groupe de Lie complexe, H un sous-groupe complexe ferme de G, et X := G/H. Soit R le radical et S un sous-groupe semi-simple maximal de G. La construction d'exemples de varietes non compactes X homogenes d'un produit semi-direct G = S × R, possedant une metrique kahlerienne pas necessairement invariante par G, a suscite ce travail. L'orbite S/S n H de S dans X est kahlerienne. Donc S n H est un sous-groupe algebrique de S [4]. La presence d'une structure kahlerienne sur X devrait… 

References

SHOWING 1-10 OF 20 REFERENCES

On Complex Homogeneous Spaces with Top Homology in Codimension Two

Abstract Define dx to be the codimension of the top nonvanishing homology group of the manifold X with coefficients in 2. We investigate homogeneous spaces X := G/H, where G is a connected complex

Invariant plurisubharmonic functions and hypersurfaces on semisimple complex Lie groups

A connected complex Lie group G is called (linear) reductive, if it is the complexification K r of a maximal compact subgroup K of G. Such a group G is up to a finite (central) covering group

The fundamental conjecture for homogeneous Kähler manifolds

Toute variete de Kahler homogene est un fibre de fibres holomorphe sur un domaine borne homogene dans lequel la fibre est (avec la metrique de Kahler induite) le produit d'une variete de Kahler

Invariant analytic hypersurfaces in complex Lie groups

  • B. Gilligan
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2004
Suppose G is a complex Lie group and H is a closed complex subgroup of G. Let G′ denote the commutator subgroup of G. If there are no nonconstant holomorphic functions on G/H and H is not contained

Homogeneous Complex Manifolds with more than One End

For homogeneous spaces of a (real) Lie group one of the fundamental results concerning ends (in the sense of Freudenthal [8] ) is due to A. Borel [6]. He showed that if X = G/H is the homogeneous

On holomorphically separable complex solv-manifolds

© Annales de l’institut Fourier, 1986, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions

On the structure of complex solvmanifolds

A connected complex space X is called a solvmanifold if there is a connected solvable complex Lie group G which acts holomorphically and transitively on it. The goal of this paper is to understand

On non-compact complex nil-manifolds

Given a complex manifold X, it is natural to consider the quotient space X~ ~, where p~q whenever f(p)=f(q) for every fe(9(X). In the best of all worlds one would hope that X / ~ is a Stein space,

Non-compact Complex Lie Groups without Non-constant Holomorphic Functions

In this paper we shall consider, on the one hand, a complex Lie group with sufficiently many holomorphic functions and, on the other hand, a complex Lie group whose holomorphic functions are

On the Discrete Subgroups and Homogeneous Spaces of Nilpotent Lie Groups

Recently A, Malcev has shown that the homogeneous space of a connected nilpotent Lie group G is the direct product of a compact space and an Euclidean-space and that the compact space of this direct