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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.
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