Geometric realizations of Hermitian curvature models

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 whic...

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Veröffentlicht in:	Journal of the Mathematical Society of Japan 2010-07, Vol.62 (3), p.851-866
Hauptverfasser:	BROZOS-VÁZQUEZ, Miguel, GILKEY, Peter, KANG, Hyunsuk, NIKČEVIĆ, Stana
Format:	Artikel
Sprache:	eng
Schlagworte:	53B20 53B35 Gray identity Hermitian manifold Kaehler identity Ricci tensor scalar curvature star-Ricci tensor star-scalar curvature Tricerri-Vanhecke curvature decomposition
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Beschreibung
Zusammenfassung:	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.
ISSN:	0025-5645 1881-2333
DOI:	10.2969/jmsj/06230851