Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A theorem on compact locally conformal Kähler manifolds

Author: Izu Vaisman
Journal: Proc. Amer. Math. Soc. 75 (1979), 279-283
MSC: Primary 53C55
MathSciNet review: 532151
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • [1] T. Aubin, Variétés hermitiennes compactes localement conformément kählériennes, C. R. Acad. Sci. Paris 261 (1965), 2427-2430. MR 0185555 (32:3021)
  • [2] -, The scalar curvature, Differential Geometry and Relativity, A Volume in Honour of A. Lichnerowicz, Reidel, Dordrecht, 1976, pp. 5-18. MR 0433500 (55:6476)
  • [3] S. I. Goldberg, Curvature and homology, Academic Press, New York, 1962. MR 0139098 (25:2537)
  • [4] S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. II, Interscience, New York, 1969. MR 0238225 (38:6501)
  • [5] I. Vaisman, On locally conformal almost Köhler manifolds, Israel J. Math. 24 (1976), 338-351. MR 0418003 (54:6048)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C55

Retrieve articles in all journals with MSC: 53C55

Additional Information

Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society