Tohoku Mathematical Journal
2026
June
SECOND SERIES VOL. 78, NO. 2

Tohoku Math. J.
78 (2026), 269-276

Title VAISMAN'S THEOREM AND LOCAL REDUCIBILITY

Author Ovidiu Preda and Miron Stanciu

(Received August 19, 2024, revised January 23, 2025)
Abstract. As proven in a celebrated theorem due to Vaisman, pure locally conformally Kähler metrics do not exist on compact Kähler manifolds. In a previous paper, we extended this result to the singular setting, more precisely to Kähler spaces which are locally irreducible. Without the additional assumption of local irreducibility, there are counterexamples for which Vaisman's theorem does not hold. In this article, we give a much broader sufficient condition under which Vaisman's theorem still holds for compact Kähler spaces which are locally reducible.

Mathematics Subject Classification. Primary 53C55; Secondary 32S45.
Key words and phrases. Kähler space, locally conformally Kähler space, locally reducible.

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