On the piecewise geodesic approximation of Andersson and Driver (Q819469)

\textit{L. Andersson} and \textit{B. Driver} [J. Funct. Anal. 165, No. 2, 430--498 (1999; Zbl 0943.58024)] proved a piecewise geodesic approximation formula for path integrals on compact Riemannian manifolds. In this context geodesics are those of the Levi-Civita connection. The author in this paper proves a generalization of the Andersson-Driver result for \(H^1\)-type metric to the case of general metric connections. Metric connections other than the Levi-Civita connection naturally appear in stochastic analysis on Lie groups and homogeneous spaces.