A restricted version of the inverse problem of Lagrangian dynamics for the canonical linear connection on a Lie group is studied. Specifically for solvable Lie algebras of dimension up to and including six all algebras for which there is a compatible pseudo-Riemannian metric on the corresponding linear Lie group are found. Of the 19 such metrics four are bi-invariant. The Lie algebras are taken from tables compiled originally by Mubarakzyanov [Izv. Vyssh. Uchebn. Zaved., Mat. 4, 104-116 (1963)] and Morozov [Izv. Vyssh. Uchebn. Zaved., Mat. 4, 161-171 (1958)].
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics