RECURRENT METRICS IN THE GEOMETRY OF SECOND ORDER DIFFERENTIAL EQUATIONS

Given a pair (semispray S, metric g) on a tangent bundle, the family of nonlinear connections N such that g is recurrent with respect to (S, N) with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair (N, g) to be recurrent as well as for the triple (S, N, g), where N is the canonical nonlinear connection of the semispray S. Also, the Weyl connection of conformal gauge theories is obtained as a particular case.