Geodesic
Invariant almost contact structures and connections on the Lobachevsky space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 47-56.

Voir la notice de l'article provenant de la source Math-Net.Ru

It has been proved that there is left-invariant normal almost contact metric structure on the group model of the Lobachevsky space. All left-invariant linear connections compatible with this structure have been found and connections with a zero curvature tensor have been distinguished among them. On the Lobachevsky space, in addition to the Levi-Civita connection, there is a 1-parameter family of metric connections with skew-torsion that is invariant with respect to the complete six-dimensional group of motions. Also, there is only one semi symmetric almost contact metric connection that is invariant with respect to a 4-dimensional subgroup of the group of motions.
Keywords: almost contact structure
Mots-clés : group of motions, invariant connection. 
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A. O. Rastrepina; O. P. Surina. Invariant almost contact structures and connections on the Lobachevsky space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 47-56. http://geodesic.mathdoc.fr/item/IVM_2023_2_a3/

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