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Compact homogeneous lcK manifolds are Vaisman

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Abstract

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

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References

  1. Hasegawa, K., Kamishima, Y.: Locally conformally Kähler structures on homogeneous spaces. arXiv:1101.3693v10 (2013)

  2. Hasegawa, K., Kamishima, Y.: Compact homogeneous locally conformally Kähler manifolds. arXiv:1312.2202v1 (2013)

  3. Moroianu, A., Ornea, L.: Homogeneous locally conformally Kähler manifolds. arXiv:1311.0671v1 (2013)

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Acknowledgments

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

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Authors and Affiliations

  1. CMLS, Ecole Polytechnique, UMR 7640 du CNRS, 91128, Palaiseau, France

    Paul Gauduchon

  2. Université de Versailles-St. Quentin, Laboratoire de Mathématiques, UMR 8100 du CNRS, 45 avenue des Etats-Unis, 78035, Versailles, France

    Andrei Moroianu

  3. Univ. of Bucharest, Faculty of Mathematics, 14 Academiei str, 70109, Bucharest, Romania

    Liviu Ornea

  4. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21, Calea Grivitei str, 010702, Bucharest, Romania

    Liviu Ornea

Authors
  1. Paul Gauduchon
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  2. Andrei Moroianu
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  3. Liviu Ornea
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Corresponding author

Correspondence to Paul Gauduchon.

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Gauduchon, P., Moroianu, A. & Ornea, L. Compact homogeneous lcK manifolds are Vaisman. Math. Ann. 361, 1043–1048 (2015). https://doi.org/10.1007/s00208-014-1103-x

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  • DOI: https://doi.org/10.1007/s00208-014-1103-x

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