Geodesic
On submanifolds with a parallel normal vector field in spaces of constant curvature
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 3-10

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In this paper, we describe normal vector fields of a special form along geodesic lines on $n$-dimensional submanifolds of $(n+p)$-dimensional spaces of constant curvature, in particular, fields of normal curvature and normal torsion of a submanifold at a point in a given direction. We study submanifolds such that these normal vector fields are parallel in the normal connection along their geodesic lines.
Keywords: submanifold, space of constant curvature, second fundamental form, normal vector field, normal curvature vector
Mots-clés : normal torsion vector. 
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     author = {I. I. Bodrenko},
     title = {On submanifolds with a parallel normal vector field in spaces of constant curvature},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {169},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_169_a0/}
}
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I. I. Bodrenko. On submanifolds with a parallel normal vector field in spaces of constant curvature. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 3-10. http://geodesic.mathdoc.fr/item/INTO_2019_169_a0/