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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A theorem on compact locally conformal Kähler manifolds


Author: Izu Vaisman
Journal: Proc. Amer. Math. Soc. 75 (1979), 279-283
MSC: Primary 53C55
DOI: https://doi.org/10.1090/S0002-9939-1979-0532151-4
MathSciNet review: 532151
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Abstract: We prove that a compact locally conformai Kähler manifold which satisfies either: (1) it has nonpositive conformal invariant $ \mu $ [2] and its local conformal Kähler metrics have nonnegative scalar curvature or (2) its local conformal Kähler (l.c.K.) metrics have a positive or negative definite Ricci form is a Kahler manifold. We conjecture that every compact l.c.K. manifold which satisfies all the topological restrictions of a Kähler manifold admits some Kähler metric.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0532151-4
Article copyright: © Copyright 1979 American Mathematical Society