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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Some curvature properties of locally conformal Kähler manifolds
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by Izu Vaisman PDF
Trans. Amer. Math. Soc. 259 (1980), 439-447 Request permission

Abstract:

Curvature identities and holomorphic sectional curvature of locally conformal Kähler manifolds are investigated. Particularly, sufficient conditions for such manifolds to be globally conformal Kähler are derived.
References
  • Samuel I. Goldberg, Curvature and homology, Pure and Applied Mathematics, Vol. XI, Academic Press, New York-London, 1962. MR 0139098
  • Alfred Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tohoku Math. J. (2) 28 (1976), no. 4, 601–612. MR 436054, DOI 10.2748/tmj/1178240746
  • S. Kobayashi and K. Nomizu, Foundations of differential geometry. II, Interscience, New York, 1969.
  • Paulette Libermann, Sur les structures presque complexes et autres structures infinitésimales régulières, Bull. Soc. Math. France 83 (1955), 195–224 (French). MR 79766, DOI 10.24033/bsmf.1460
  • Izu Vaisman, On locally conformal almost Kähler manifolds, Israel J. Math. 24 (1976), no. 3-4, 338–351. MR 418003, DOI 10.1007/BF02834764
  • —, Locally conformal Kähler manifolds with parallel Lee form, Rend. Mat. (to appear).
  • Izu Vaisman, Remarkable operators and commutation formulas on locally conformal Kähler manifolds, Compositio Math. 40 (1980), no. 3, 287–299. MR 571051
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 259 (1980), 439-447
  • MSC: Primary 53C55
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0567089-2
  • MathSciNet review: 567089