Open AccessMathematical modeling in the study of semisymmetric connections on three-dimensional Lie groups with the metric of the Ricci soliton
Author(s) -
Павел Николаевич Клепиков,
E. D. Rodionov,
O. P. Khromova
Publication year - 2021
Publication title -
vestnik ûgorskogo gosudarstvennogo universiteta
Language(s) - English
Resource type - Journals
eISSN - 2078-9114
pISSN - 1816-9228
DOI - 10.17816/byusu20210123-29
Subject(s) - unimodular matrix , lie group , mathematics , invariant (physics) , pure mathematics , connection (principal bundle) , ricci curvature , metric (unit) , algebra over a field , mathematical analysis , mathematical physics , geometry , operations management , curvature , economics
Semisymmetric connections were first discovered by E. Cartan and are a natural generalization of the Levi-Civita connection. The properties of the parallel transfer of such connections and the basic tensor fields were investigated by I. Agrikola, K. Yano and other mathematicians. In this paper, a mathematical model is constructed for studying semisymmetric connections on three-dimensional Lie groups with the metric of an invariant Ricci soliton. A classification of these connections on three-dimensional unimodular Lie groups with left-invariant Riemannian metric of the Ricci soliton is obtained. It is proved that in this case there are nontrivial invariant semisimetric connections. Previously, the authors carried out similar studies in the class of Einstein metrics.