Geodesic
Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 937-949.

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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.
DOI : 10.1007/s10587-012-0075-9
Classification : 53C05, 53C15, 53C55
Keywords: natural lift; cotangent bundle; almost product structure; para-Hermitian structure; para-Kähler structure 
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Druţă-Romaniuc, Simona-Luiza. Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 937-949. doi : 10.1007/s10587-012-0075-9. http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0075-9/

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