A difference approximation of the covariant derivative and other operators and geometric objects given in a Riemannian domain

摘要

Difference approximations for covariant derivatives of tensorfields of arbitrary rank given in Riemannian domain, retaining maingeometrical properties, are suggested. An approach to its constructionis based on certain difference analogs for Christoffel symbols. The maincriterium here is exact vanishing for a difference covariant derivative offundamental tensor and, in addition, an exact approximation of commutationrelations which is possible only at a certain developed in the paperdifference approximations for the curvature tensor.