Hyperspheres in Euclidean and Minkowski 4-spaces as almost paracontact almost paracomplex Riemannian manifolds

Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds are investigated. An example is commented as support of obtained results.

Matrix Lie Groups as 3-Dimensional Almost Paracontact Almost Paracomplex Riemannian Manifolds

Lie groups considered as three-dimensional almost paracontact almost paracomplex Riemannian manifolds are investigated. In each basic class of the classification used for the manifolds under consideration, a correspondence is established between the Lie algebra and the explicit matrix representation of its Lie group.

几乎para接触几乎para复黎曼流形作为二维空间形式的扩张

Almost paracontact almost paracomplex Riemannian manifolds as extensions of 2-dimensional space-forms

本文研究最低维几乎para接触黎曼流形，其构造为实线与二维空间形式的乘积，度量由锥度量或双曲扩张得到，并依据分类与曲率性质加以刻画。

On Almost Paracontact Almost Paracomplex Riemannian Manifolds

Almost paracontact manifolds of an odd dimension having an almost paracomplex structure on the paracontact distribution are studied. The components of the fundamental (0,3)-tensor, derived by the covariant derivative of the structure endomorphism and the metric on the considered manifolds in each of the basic classes, are obtained. Then, the case of the lowest dimension 3 of these manifolds is considered. An associated tensor of the Nijenhuis tensor is introduced and the studied manifolds are characterized with respect to this pair of tensors. Moreover, cases of paracontact and para-Sasakian t…

Pair of associated Schouten-van Kampen connections adapted to an almost paracontact almost paracomplex Riemannian structure

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the paracontact distribution and an almost paracontact almost paracomplex Riemannian structure generated by the pair of associated metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic classes of the manifolds with the considered structure are characterized. Curvature properties of the studied connections are obtained. A family of examples on a Lie group is constructed.

Lifts of Lorentzian r- Paracontact Structure: A Geometrical Dynamics Meaning

The goal of this paper, using lifting theory it is to produce almost paracomplex struc- tures on the tangent bundle of almost Lorentzian r-paracontact manifold endowed with almost Lorentzian r-paracontact structure. Finally, we discuss the effect over dynamics systems of the produced geometrical structures.