Geometric Realizations of Hermitian curvature models

M. Brozos-Vazquez, P. Gilkey, H. Kang, S. Nikcevic

Published 2008-12-15Version 1

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.