Resumen de Inverse problem for the canonical Lie group connection

I. Strugar, G. Thompson

• The geodesic spray of the canonical symmetric connection for a five dimensional Lie group is studied. For each corresponding Lie algebra a faithful representation in terms of vector fields on a five dimensional real space is obtained, thereby providing an effective realization of Lie's third theorem. Thereafter the inverse problem of the calculus of variations for each of the geodesic sprays is investigated. In all cases it is determined whether such spray is of Euler-Lagrange type and in the affirmative case at least one concrete Lagrangian is written down. All the cases where there is a Lagrangian of metric type are exhibited.