Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On locally and globally conformal Kähler manifolds


Author: Izu Vaisman
Journal: Trans. Amer. Math. Soc. 262 (1980), 533-542
MSC: Primary 53C55; Secondary 53B35
MathSciNet review: 586733
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C55, 53B35

Retrieve articles in all journals with MSC: 53C55, 53B35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0586733-7
PII: S 0002-9947(1980)0586733-7
Article copyright: © Copyright 1980 American Mathematical Society