Geodesic
On the invariant correspondence between the symmetric second-rank tensors and the vector systems
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 69-74

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We discuss the possibilities of various representations of high-rank tensors in three-dimensional space using lower-rank tensors, in particular, the representations of second-rank tensors by vector fields. The purpose of these representations is a convenient geometric interpretation of certain mechanical properties of objects described by high-rank tensors. We propose an invariant correspondence of symmetric tensors of the second rank in three-dimensional space and pairs of vectors from the same space. On the basis of this correspondence, a geometric interpretation of the action of an isotropic symmetric tensor function of a tensor argument is given. 
@article{VMUMM_2021_3_a10,
     author = {D. V. Georgievskii},
     title = {On the invariant correspondence between the symmetric second-rank tensors and the vector systems},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {69--74},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a10/}
}
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D. V. Georgievskii. On the invariant correspondence between the symmetric second-rank tensors and the vector systems. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 69-74. http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a10/