An obstruction to homogeneous manifolds being Kähler

  title={An obstruction to homogeneous manifolds being K{\"a}hler},
  author={B Gilligan},
  journal={Annales de l'Institut Fourier},
  • 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… 



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