Geodesic
Classification of Two-Dimensional Surfaces with Zero Normal Torsion in Four-Dimensional Spaces of Constant Curvature
Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 744-756

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We introduce the notion of normal torsion of a surface at a point along a given direction in a Riemannian space. We give a complete classification of surfaces in four-spaces of constant curvature having zero normal torsion. 
@article{MZM_2004_75_5_a10,
     author = {V. T. Fomenko},
     title = {Classification of {Two-Dimensional} {Surfaces} with {Zero} {Normal} {Torsion} in {Four-Dimensional} {Spaces} of {Constant} {Curvature}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {744--756},
     publisher = {mathdoc},
     volume = {75},
     number = {5},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a10/}
}
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V. T. Fomenko. Classification of Two-Dimensional Surfaces with Zero Normal Torsion in Four-Dimensional Spaces of Constant Curvature. Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 744-756. http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a10/