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On Submanifolds with a Parallel Normal Vector Field in Spaces of Constant Curvature

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Abstract

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.

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Authors and Affiliations

  1. “Interactive Systems” LLC, Volgograd, Russia

    I. I. Bodrenko

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  1. I. I. Bodrenko
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Correspondence to I. I. Bodrenko.

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Dedicated to Professor V. T. Fomenko

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 169, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part II, 2019.

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Bodrenko, I.I. On Submanifolds with a Parallel Normal Vector Field in Spaces of Constant Curvature. J Math Sci 263, 351–358 (2022). https://doi.org/10.1007/s10958-022-05930-9

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  • DOI: https://doi.org/10.1007/s10958-022-05930-9

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