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Mathematische Annalen

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

Compact homogeneous lcK manifolds are Vaisman

  • Paul Gauduchon
  • Andrei Moroianu
  • Liviu Ornea
Article

Abstract

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

Keywords

Manifold Vector Field Linear Isomorphism Hermitian Structure Hermitian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was partially supported by the LEA Math-Mode.

References

  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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