Tensor approach to averaging Jacobi fields along geodesicswith random curvature

The paper considers a Jacobi field along a geodesic on a Riemannian manifold on which the curvature is a stochastic process. We introduce the concept of a linearizing tensor formiung the base of derivation of the equations for $2$, $3$ and $4$-order moments. A theorem on the general form of the moment equation is proved.