A theorem on compact locally conformal Kähler manifolds

Vaisman, Izu

doi:10.1090/S0002-9939-1979-0532151-4

A theorem on compact locally conformal Kähler manifolds
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Proc. Amer. Math. Soc. 75 (1979), 279-283 Request permission

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.

References

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