Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 2, pp. 192-202   https://doi.org/10.15407/mag15.02.192     ( to contents , go back )
https://doi.org/10.15407/mag15.02.192

On the Structure of Multidimensional Submanifolds with Metric of Revolution in Euclidean Space

Alexander A. Borisenko

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: aborisenk@gmail.com

Received December 14, 2017, revised June 6, 2018.

Abstract

It is proved that a submanifold of low codimension with induced metric of revolution of sectional curvature of constant sign is a submanifold of revolution if the coordinate geodesic lines are the lines of curvature.

Mathematics Subject Classification 2000: 53B25.
Key words: Metric of revolution, submanifolds of rotation, lines of curvature, sectional curvature.

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