Geodesic
The Theorem about Tensor Relation at any $N$-Dimential Pseudo-Riemannian Space
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 16-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is considered any $N $-dimential pseudo-Riemannian space $R^N_{P, N-P}$, with some second rank tensor $\Psi_{ik}(x)$. We established and proved important tensor relation such that second rank tensor and them invariants are satisfyed. We use the axial tensor of Levi–Chivita for proving these relation. It is shown that there are others useful tensor relations.
Keywords: pseudo-rimannian space, Levi–Chivita tensor, tensor relation, invariants of second rank tensor. 
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P. A. Vshivtseva; I. P. Denisova; M. M. Denisov. The Theorem about Tensor Relation at any $N$-Dimential Pseudo-Riemannian Space. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 16-22. http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a1/

[1] Denisova I. P., Dalal M., “Development of the Method of Potentials for the Problems of Gravitation-Electromagnetic Conversion”, J. of Mathematical Physics, 38:11 (1997), 5820–5832 | DOI | MR | Zbl

[2] Denisov V. I., Svertilov S. I., “Nonlinear Electrodynamic and Gravitational Actions of the Neutron Star Fields on the Propagation of the Electromagnetic Waves”, Physical Review. Part D, 71:6 (2005), 063002-1–063002-13 | DOI | MR

[3] Denisova I. P., “Razvitie metoda spinovykh koeffitsientov dlya integrirovaniya uravnenii biometricheskikh teorii gravitatsii”, Dif. uravneniya, 35:7 (1999), 935–941 | MR | Zbl

[4] Landau L. D., Lifshits E. M., Teoriya polya, 7-e izd., Nauka, M., 1988 | MR

[5] Denisova I. P., Krivchenkov I. V., Vshivtseva P. A. et al., “Nonlinear Gravitational-electromagnetic Bending of the Rays of Weak Electromagnetic Waves in the Fields of Pulsars and Magnetars”, General Relativity and Gravitation, 36:4 (2004), 889–898 | DOI

[6] Krivchenkov I. V., “Razvitie metoda eikonala v nelineinoi elektrodinamike na osnove printsipa geometrizatsii”, Teoreticheskaya i matematicheskaya fizika, 150:1 (2007), 112–117 | DOI | MR | Zbl