Compact lcK manifolds with parallel vector fields

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.

Abstract licence: CC BY

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