Mathematische Annalen

, Volume 361, Issue 3–4, pp 1043–1048 | Cite as

Compact homogeneous lcK manifolds are Vaisman

  • Paul GauduchonEmail author
  • Andrei Moroianu
  • Liviu Ornea


We prove that any compact homogeneous locally conformally Kähler manifold has parallel Lee form.


Manifold Vector Field Linear Isomorphism Hermitian Structure Hermitian Manifold 
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This work was partially supported by the LEA Math-Mode.


  1. 1.
    Hasegawa, K., Kamishima, Y.: Locally conformally Kähler structures on homogeneous spaces. arXiv:1101.3693v10 (2013)
  2. 2.
    Hasegawa, K., Kamishima, Y.: Compact homogeneous locally conformally Kähler manifolds. arXiv:1312.2202v1 (2013)
  3. 3.
    Moroianu, A., Ornea, L.: Homogeneous locally conformally Kähler manifolds. arXiv:1311.0671v1 (2013)

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.CMLS, Ecole Polytechnique, UMR 7640 du CNRSPalaiseauFrance
  2. 2.Université de Versailles-St. Quentin, Laboratoire de Mathématiques, UMR 8100 du CNRSVersaillesFrance
  3. 3.Univ. of Bucharest, Faculty of MathematicsBucharestRomania
  4. 4.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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