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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...
In this paper we present new examples of -dimensional compact cosymplectic manifolds which are not topologically equivalent to the canonical examples, i.e., to the product of the -dimensional real torus and the -dimensional complex projective space, with and These new examples are compact solvmanifolds and they are constructed as suspensions with fibre the -dimensional real torus. In the particular case using the examples obtained, we conclude that a -dimensional compact flat orientable...
We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.
Using the fundamental notions of the quaternionic analysis we show that there are no 4-dimensional almost Kähler manifolds which are locally conformally flat with a metric of a special form.
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