Geometric Realizations of para-Hermitian curvature models

M. Brozos-Vazquez; P. Gilkey; S. Nikcevic; R. Vazquez-Lorenzo

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arXiv · 0902.1697

Geometric Realizations of para-Hermitian curvature models

M. Brozos-Vazquez·P. Gilkey·S. Nikcevic·R. Vazquez-Lorenzo

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Abstract

We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen to have constant scalar curvature and constant *-scalar curvature.

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M. Brozos-Vazquez, P. Gilkey, S. Nikcevic, R. Vazquez-Lorenzo. 2009-02-10. Geometric Realizations of para-Hermitian curvature models. https://arxiv.org/abs/0902.1697

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