Posted in: . High . Learning. head. North Caucasus Region . Natural Sciences (2003). Special Issue: Nonlinear Solid Environment Mechanics Problems: C. 176 - 195. The article presents a modified theory of tensor symmetry, including non-Euclidean tensors. Polar (Euclidean) and axial (non-Euclidean) tensors . are considered. Proposed new definition of tensor invariants. It is shown that any invariant is a solution of some differential equation of the first order. The number of independent solutions of these equations determines the minimum number of invariants needed to fix the tensor system to the accuracy of a hard turn.