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Invariant Almost Contact Structures and Connections on the Lobachevsky Space

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Abstract

It has been proven that there is a 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 semisymmetric almost contact metric connection that is invariant with respect to a four-dimensional subgroup of the group of motions.

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Authors and Affiliations

  1. Penza State University, 440026, Penza, Russia

    A. O. Rastrepina & O. P. Surina

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  1. A. O. Rastrepina
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  2. O. P. Surina
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Correspondence to A. O. Rastrepina or O. P. Surina.

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Rastrepina, A.O., Surina, O.P. Invariant Almost Contact Structures and Connections on the Lobachevsky Space. Russ Math. 67, 43–51 (2023). https://doi.org/10.3103/S1066369X23020056

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  • DOI: https://doi.org/10.3103/S1066369X23020056

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