On locally and globally conformal kahler manifolds

Izu Vaisman

doi:10.1090/S0002-9947-1980-0586733-7

On locally and globally conformal kahler manifolds

Izu Vaisman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Some relations between the locally conformal Kahler (l-c.K.) and the globally conformal Kahler (g.c.K.) properties are established. Compact l.c.K. manifolds which are not g.c.K. do not have Kahler 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 gx.K. has at least one odd odd-dimensional Betti number.

Original language	English
Pages (from-to)	533-542
Number of pages	10
Journal	Transactions of the American Mathematical Society
Volume	262
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1980-0586733-7
State	Published - Dec 1980

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1980-0586733-7

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AB - Some relations between the locally conformal Kahler (l-c.K.) and the globally conformal Kahler (g.c.K.) properties are established. Compact l.c.K. manifolds which are not g.c.K. do not have Kahler 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 gx.K. has at least one odd odd-dimensional Betti number.

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On locally and globally conformal kahler manifolds

Abstract

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