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Complex Manifolds

Ed. by Fino, Anna Maria

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Mathematical Citation Quotient (MCQ) 2016: 0.67


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2300-7443
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Compact lcK manifolds with parallel vector fields

Andrei Moroianu
  • Corresponding author
  • Université de Versailles-St Quentin, Laboratoire de Mathématiques, UMR 8100 du CNRS, 45 avenue des États-Unis, 78035 Versailles, France
  • Other articles by this author:
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Published Online: 2015-07-09 | DOI: https://doi.org/10.1515/coma-2015-0004

Abstract

We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.

Keywords: Vaisman manifolds; lcK manifolds; parallel vector fields

References

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  • [4] P. Gauduchon, A. Moroianu, L. Ornea, Compact homogeneous lcK manifolds are Vaisman, Math. Ann. 361 (3-4), (2015), 1043– 1048. Web of ScienceGoogle Scholar

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About the article

Received: 2015-05-13

Accepted: 2015-05-30

Published Online: 2015-07-09


Citation Information: Complex Manifolds, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0004.

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© 2015 Andrei Moroianu. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

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[1]
Cornelia Livia Bejan and Mircea Crasmareanu
International Journal of Geometric Methods in Modern Physics, 2017, Volume 14, Number 02, Page 1750023
[2]
Andrei Moroianu and Sergiu Moroianu
International Mathematics Research Notices, 2016, Page rnw151

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