Geodesic
Eigenvalue problem for some tensors used in mechanics and a number of essential compatibility conditions for the Saint-Venant deformation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2017), pp. 54-58

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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. 
@article{VMUMM_2017_3_a7,
     author = {M. U. Nikabadze},
     title = {Eigenvalue problem for some tensors used in mechanics and a number of essential compatibility conditions for the {Saint-Venant} deformation},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {54--58},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_3_a7/}
}
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M. U. Nikabadze. Eigenvalue problem for some tensors used in mechanics and a number of essential compatibility conditions for the Saint-Venant deformation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2017), pp. 54-58. http://geodesic.mathdoc.fr/item/VMUMM_2017_3_a7/