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Nambu-Poisson Tensors on Lie Groups

Nobutada Nakanishi (2000)

Banach Center Publications

First as an application of the local structure theorem for Nambu-Poisson tensors, we characterize them in terms of differential forms. Secondly left invariant Nambu-Poisson tensors on Lie groups are considered.

Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles

Simona-Luiza Druţă-Romaniuc (2012)

Czechoslovak Mathematical Journal

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...

Natural transformations between T²₁T*M and T*T²₁M

Miroslav Doupovec (1991)

Annales Polonici Mathematici

We determine all natural transformations T²₁T*→ T*T²₁ where T k r M = J 0 r ( k , M ) . We also give a geometric characterization of the canonical isomorphism ψ₂ defined by Cantrijn et al.

Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

Josef Janyška (2001)

Archivum Mathematicum

Let M be a differentiable manifold with a pseudo-Riemannian metric g and a linear symmetric connection K . We classify all natural (in the sense of [KMS]) 0-order vector fields and 2-vector fields on T M generated by g and K . We get that all natural vector fields are of the form E ( u ) = α ( h ( u ) ) u H + β ( h ( u ) ) u V , where u V is the vertical lift of u T x M , u H is the horizontal lift of u with respect to K , h ( u ) = 1 / 2 g ( u , u ) and α , β are smooth real functions defined on R . All natural 2-vector fields are of the form Λ ( u ) = γ 1 ( h ( u ) ) Λ ( g , K ) + γ 2 ( h ( u ) ) u H u V , where γ 1 , γ 2 are smooth real functions defined...

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