On the Theory of Covariant Differentiation of Two Point Pseudotensor Fields

In this paper, the problems of covariant differentiation of two-point pseudotensor fields of arbitrary ranks and weights are considered and discussed. The requisite equations and notions from algebra and analysis of pseudotensors are recalled. The notion of a two-point pseudotensor field is introduced, based on the equation for its transformation under changing coordinate net. An equation for the transformation of a two-point pseudotensor field to a two-point absolute tensor field is proposed. Definitions of total and explicit operators of partial and covariant differentiation of two-point pseudotensors are introduced. Equations for covariant derivatives of a two-point pseudotensor field are obtained. Important examples of two-point pseudotensor fields from non-linear solid mechanics are noted.