On vertical skew symmetric almost contact 3-structures |
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Authors: | Adela Mihai Radu Rosca |
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Institution: | (1) Faculty of Mathematics, , Str. Academiei 14, 010014 Bucharest, Romania;(2) 59 Avenue Emile Zola, 75015 Paris, France |
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Abstract: | We consider a (2m + 3)-dimensional Riemannian manifold M(ξ r, ηr, g ) endowed with a vertical skew symmetric almost contact 3-structure. Such manifold is foliated by 3-dimensional submanifolds
of constant curvature tangent to the vertical distribution and the square of the length of the vertical structure vector
field is an isoparametric function. If, in addition, M(ξ r, ηr, g ) is endowed with an f -structure φ, M, turns out to be a framed f−CR-manifold. The fundamental 2-form Ω associated with φ is a presymplectic form. Locally, M is the Riemannian product
of two totally geodesic submanifolds, where
is a 2m-dimensional Kaehlerian submanifold and
is a 3-dimensional submanifold of constant curvature. If M is not compact, a class of local Hamiltonians of Ω is obtained. |
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Keywords: | 53C15 53D15 53C25 |
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