Recurrent metrics in the geometry of second order differential equations

Document Type : Research Paper


Faculty of Mathematics University "Al. I. Cuza" Iasi, 700506


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 $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$
is the canonical nonlinear connection of the semispray $S$. Also,
the Weyl connection of conformal gauge theories is obtained as a particular