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. 
@article{IVM_2023_2_a3,
     author = {A. O. Rastrepina and O. P. Surina},
     title = {Invariant almost contact structures and connections on the {Lobachevsky} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {47--56},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_2_a3/}
}
TY  - JOUR
AU  - A. O. Rastrepina
AU  - O. P. Surina
TI  - Invariant almost contact structures and connections on the Lobachevsky space
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 47
EP  - 56
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_2_a3/
LA  - ru
ID  - IVM_2023_2_a3
ER  - 
%0 Journal Article
%A A. O. Rastrepina
%A O. P. Surina
%T Invariant almost contact structures and connections on the Lobachevsky space
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 47-56
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_2_a3/
%G ru
%F IVM_2023_2_a3
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/