Tensor Approach to Averaging Jacobi Fields along Geodesics with Random Curvature / Grachev D.A. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. ? 5. P. 58-61 [Moscow Univ. Math. Bulletin. Vol. 65, No 5, 2010. P. 213-216].

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

Key words: Jacobi field, differential equation with random coefficients, statistical moment.