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Transactions of the American Mathematical Society

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On locally and globally conformal Kähler manifolds


Author: Izu Vaisman
Journal: Trans. Amer. Math. Soc. 262 (1980), 533-542
MSC: Primary 53C55; Secondary 53B35
DOI: https://doi.org/10.1090/S0002-9947-1980-0586733-7
MathSciNet review: 586733
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Abstract: Some relations between the locally conformal Kähler (l.c.K.) and the globally conformal Kähler (g.c.K.) properties are established. Compact l.c.K. manifolds which are not g.c.K. do not have Kähler metrics. l.c.K. manifolds which are not g.c.K. are analytically irreducible. Various curvature restrictions on l.c.K. manifolds imply the g.c.K. property. Total spaces of induced Hopf fibrations are l.c.K. and not g.c.K. manifolds.

Conjecture. A compact l.c.K. manifold which is not g.c.K. has at least one odd odd-dimensional Betti number.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0586733-7
Article copyright: © Copyright 1980 American Mathematical Society

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