Geometric realizations of Hermitian curvature models

Miguel Brozos-Vázquez; Peter Gilkey; Hyunsuk Kang; Stana Nikcevic

doi:10.2969/jmsj/06230851

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Geometric realizations of Hermitian curvature models

Miguel Brozos-Vázquez, Peter Gilkey, Hyunsuk Kang, Stana Nikcevic

著者情報

キーワード: Gray identity, Hermitian manifold, Kaehler identity, Ricci tensor, scalar curvature, $\star$-Ricci tensor, $\star$-scalar curvature, Tricerri-Vanhecke curvature decomposition

ジャーナルフリー

2010 年 62 巻 3 号 p. 851-866

DOI https://doi.org/10.2969/jmsj/06230851

詳細

抄録

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 $\star$-scalar curvature which satisfies the Kaehler condition at the point in question.