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Compact homogeneous lcK manifolds are Vaisman

Abstract

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

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References

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

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

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    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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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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Keywords

  • Manifold
  • Vector Field
  • Linear Isomorphism
  • Hermitian Structure
  • Hermitian Manifold