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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On locally and globally conformal Kähler manifolds
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by Izu Vaisman PDF
Trans. Amer. Math. Soc. 262 (1980), 533-542 Request permission

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
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • 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