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On Riemann-Poisson Lie groups

Brahim Alioune, Mohamed Boucetta, Ahmed Sid’Ahmed Lessiad (2020)

Archivum Mathematicum

A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in [4]. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.

On some properties of induced almost contact structures

Zuzanna Szancer (2015)

Annales Polonici Mathematici

Real affine hypersurfaces of the complex space n + 1 with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of the induced almost contact structures are proved. In particular, we prove some properties of the induced structure when the distribution is involutive. Some constraints on a shape operator when the induced almost contact structure is either normal or ξ-invariant are also given.

On the Cartan-Norden theorem for affine Kähler immersions

Maria Robaszewska (2000)

Annales Polonici Mathematici

In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.

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