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Keywords:
natural lift; cotangent bundle; almost product structure; para-Hermitian structure; para-Kähler structure
natural lift; cotangent bundle; almost product structure; para-Hermitian structure; para-Kähler structure
Summary:
We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. Studying the compatibility and the anti-compatibility relations between the determined structures and a natural diagonal metric, we find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. Finally, we prove the characterization theorem for the natural diagonal (almost) para-Kählerian structures on the total space of the cotangent bundle.
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