Abstract:
Several questions related to the problem on the eigenvalues of the tensor $\begin{smallmatrix}
\displaystyle{}\\
\overset{\vphantom{p}}{\stackrel{\displaystyle\mathbf A}{\stackrel{\sim}{\sim}}}\\
\end{smallmatrix}\in\mathbb R_4(\Omega)$ with special symmetries are considered. Here $\Omega$ is a certain region of, in general, four-dimensional (three-dimensional) Riemann space. It is proved that in this case a non-degenerate tensor of the fourth rank in the case of a four-dimensional (three-dimensional) Riemann space has no more than six (three) essential components. It is shown that the number of essential conditions of deformation Saint-Venant compatibility less than six.
Key words:compatibility conditions, strain tensor, incompatibility tensor, stress tensor, eigentensor, complete orthonormal system of eigentensors, symbol of anisotropy, symbol of structure.
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