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Complex Manifolds

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Mathematical Citation Quotient (MCQ) 2015: 1.20


Emerging Science

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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
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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  • [2] N. Buchdahl, On compact Kähler surfaces, Ann. Inst. Fourier 49 no. 1 (1999), 287–302. [Crossref]

  • [3] S. Dragomir, L. Ornea, Locally conformal Kähler geometry, Progress in Math. 155, Birkhäuser, Boston, Basel, 1998.

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

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  • [7] L. Ornea, M. Verbitsky, Structure theorem for compact Vaisman manifolds, Math. Res. Lett., 10 (2003), 799–805.

  • [8] I. Vaisman, A survey of generalizedHopf manifolds, Rend. Sem.Mat. Univ. Politec. Torino 1983, Special Issue (1984), 205–221.

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. Export Citation

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

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