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Invariant almost contact structures and connections on the Lobachevsky space
A. O. Rastrepina, O. P. Surina Penza State University, 40 Krasnay str., Penza, 440026 Russia
Abstract:
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, group of motions, invariant connection.
Received: 29.03.2022 Revised: 13.07.2022 Accepted: 28.09.2022
Citation:
A. O. Rastrepina, O. P. Surina, “Invariant almost contact structures and connections on the Lobachevsky space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 2, 47–56; Russian Math. (Iz. VUZ), 67:2 (2023), 43–51
Linking options:
https://www.mathnet.ru/eng/ivm9853 https://www.mathnet.ru/eng/ivm/y2023/i2/p47
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Abstract page: | 85 | Full-text PDF : | 5 | References: | 15 | First page: | 9 |
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