On submanifolds with a parallel normal vector field in spaces of constant curvature. (English. Russian original) Zbl 1489.53028

Bodrenko, I. I.

J. Math. Sci., New York 263, No. 3, 351-358 (2022); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 169, 3-10 (2019).

Summary: 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.

MSC:

53B25	Local submanifolds
53C40	Global submanifolds

Keywords:

submanifold; space of constant curvature; second fundamental form; normal vector field; normal curvature vector; normal torsion vector

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