Geodesible vector fields and adapted invariant Riemannian metrics

Gabriel-Teodor Pripoae, Cristina-Liliana Pripoae
In [8], we studied the existence of geodesible left invariant vector fields on Lie groups, with respect to left invariant Riemannian metrics. Accordingly, seven distinct types of specific behaviours led to a classification of Lie groups, through linear algebraic conditions. We prove now that three of these types do not exist, so the respective classification has exactly four classes. The type I Lie groups (such that all their left invariant vector fields are geodesible) are completely
more » ... ompletely characterized as semi-direct products of solvable groups satisfying the property (Im), with compact Lie groups. We introduce some new linear algebraic invariants (the geodesic height and the geodesic dimensions), which provide geometrically inspired classifications of the Lie groups. M.S.C. 2000: 53C22, 22E15, 37C10, 15A03.