Geodesic
Fully geodetic surfaces in Riman orthogonal composition spaces
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1990), pp. 37-42 
L. Syaotzin; L. A. Matevosyan. Fully geodetic surfaces in Riman orthogonal composition spaces. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1990), pp. 37-42. http://geodesic.mathdoc.fr/item/UZERU_1990_2_a4/
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     title = {Fully geodetic surfaces in {Riman} orthogonal composition spaces},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The surfaces $X_m=X_{m_1}+X_{m_2}$ are considered in Riman space $V_n$ admitting two multiform compositions with fully orthogonal transversal positions $V_{n_1}$ and $V_{n_2}$, where $X_{m_1}$ is fully geodetic surface in $V_{n_1}$ and $X_{m_2}$ f.g.s. in $V_{n_2}$. The basic values of surface $X_m$ have also been found and the following statement is proved: in order all the surfaces be completely geodetic, it is necessary and sufficient $V_n$ being reduced space.

[1] A. P. Norden, “Prostranstva dekartovoi kompozitsii”, Izv. vuzov. Matematika, 1963, no. 4, 117–128 | MR | Zbl

[2] L. A. Matevosyan, “O putevykh poverkhnostyakh kompozitsii rimanovykh prostranstv”, Izv. vuzov. Ser. matem., 1984, no. 4, 78–80 | MR | Zbl

[3] L. P. Eizenkhart, Rimanova geometriya, IL, M., 1948 | MR | Zbl

[4] G. I. Kruchkovich, “O dvizheniyakh v subproektivnykh prostranstvakh V. F. Kagana”, Nauchn. dokl. vysshei shkoly, Fiz.-matem. nauki, 1958, 43–47 | Zbl