Vaisman theorem for LCK spaces

Abstract

. Vaisman’s theorem for locally conformally K¨ahler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a K¨ahler metric is, in fact, globally conformally K¨ahler (gcK). In this paper, we extend this theorem to compact complex spaces with singularities. PN-III-P1-1.1-TE-2019-0262, within PNCDI III. Miron Stanciu was partially supported by a grant of Ministry of Research and Inno-vation, CNCS - UEFISCDI, project no. PN-III-P4-ID-PCE-2020-0025, within PNCDI III.