On covariant non-constancy of distortion and inversed distortion tensors

Abstract

The paper deals with covariant constancy problem for tensors and pseudotensors of an arbitrary rank and weight in an Euclidean space. Requisite preliminaries from pseudotensor algebra and analysis are given. The covariant constancy of pseudotensors are separately considered. Important for multidimensional geometry examples of covariant constant tensors and pseudotensors are demonstrated. In particular, integer powers of the fundamental orienting pseudoscalar satisfied the condition of covariant constancy are introduced and discussed. The paper shows that the distortion and inversed distortion tensors are not actually covariant constant, contrary to the statements of those covariant constancy which can be found in literature on continuum mechanics.

Keywords

• pseudotensor
• fundamental orienting pseudoscalar
• distortion
• inversed distortion
• covariant constant tensors
• parallel vector field