pseudotensor, fundamental orienting pseudoscalar, permutation symbol, covariant derivative, gradient, unconventionally isotropic tensor, fully isotropic tensor, demitropic tensor, hemitropic tensor, semi-isotropic tensor, conventionally isotropic tensor, tensor with constant components, constitutive pseudotensor, chiral media, micropolar hemitropic continuum

In this paper, we discuss the covariant constancy of tensors and pseudotensors (including two-point ones) of arbitrary valency and weight in Euclidean space. The requisite notions and equations from algebra and analysis of pseudotensors in Euclidean spaces are given. The general conditions for the covariant constancy of pseudotensors are highlighted. Examples of covariantly constant tensors and pseudotensors from multidimensional geometry are considered. In particular, a fundamental orienting pseudoscalar whose integer powers satisfy the condition of covariant constancy is introduced. The properties and methods of coordinate representation of covariantly constant tensors and pseudotensors of the fourth rank are discussed. Based on an unconventional definition of a semi-isotropic tensor of the fourth rank, a coordinate representation in terms of Kronecker deltas and metric tensors is given. Conditions for the covariant constancy of semi-isotropic tensors of the fourth rank are derived.

Evgenii V. Murashkin, Cand. Sc., PhD, MD, Senior Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences,

101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.

Yuri N. Radayev, D. Sc., PhD, MSc, Professor of Continuum Mechanics, Leading Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.