Geometric realizations of Hermitian curvature models
Miguel BROZOS-VÁZQUEZ, Peter GILKEY, Hyunsuk KANG, and Stana NIKČEVIĆ
Source: J. Math. Soc. Japan Volume 62, Number 3
(2010), 851-866.
Abstract
We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature model can in fact be realized by a Hermitian manifold of constant scalar curvature and constant -scalar curvature which satisfies the Kaehler condition at the point in question.
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Keywords: Gray identity; Hermitian manifold; Kaehler identity; Ricci tensor; scalar curvature; star-Ricci tensor; star-scalar curvature; Tricerri-Vanhecke curvature decomposition
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1280496821
Digital Object Identifier: doi:10.2969/jmsj/06230851
Mathematical Reviews number (MathSciNet): MR2648064
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