Para-Kahler tangent bundles of constant para-holomorphic sectional curvature
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Abstract:
We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagonal (almost) para-K"ahlerian structures on the tangent bundle, and we study the conditions under which they have constant para-holomorphic sectional curvature.
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Journal title
volume 38 issue 4
pages 955- 972
publication date 2012-12-15
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