Geodesic
Some properties of two-dimensional surfaces with zero normal torsion in $E^4$
Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 251-265 Cet article a éte moissonné depuis la source Math-Net.Ru

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In four-dimensional Euclidean space $E^4$ the author considers two-dimensional class $C^3$ surfaces having zero normal torsion at every point and in every direction. A necessary and sufficient condition is established for such surfaces to belong to a certain hyperplane. Bibliography: 3 titles. 
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V. T. Fomenko. Some properties of two-dimensional surfaces with zero normal torsion in $E^4$. Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 251-265. http://geodesic.mathdoc.fr/item/SM_1979_35_2_a6/

[1] E. Kartan, Rimanova geometriya v ortogonalnom repere, izd-vo MGU, Moskva, 1960

[2] S. B. Kadomtsev, “Issledovanie nekotorykh svoistv normalnogo krucheniya dvumernoi poverkhnosti v chetyrekhmernom prostranstve”, Itogi nauki i tekhniki. Problemy geometrii, 7, VINITI, Moskva, 1975, 267–278 | MR | Zbl

[3] E. Bompiani, “Studi sugli spazi curvi. La seconda forma fondamentale di una $V_m$ in $V_n$”, Atti del Ist. Veneto, 80 (1920–1921), 1113–1145