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.
@article{bwmeta1.element.doi-10_1515_coma-2015-0004,
author = {Andrei Moroianu},
title = {Compact lcK manifolds with parallel vector fields},
journal = {Complex Manifolds},
volume = {2},
year = {2015},
zbl = {1320.32024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2015-0004}
}
Andrei Moroianu. Compact lcK manifolds with parallel vector fields. Complex Manifolds, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2015-0004/
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