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JOURNALS // Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry] // Archive

Zh. Mat. Fiz. Anal. Geom., 2019 Volume 15, Number 2, Pages 192–202 (Mi jmag722)

This article is cited in 6 papers

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

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.

Key words and phrases: metric of revolution, submanifolds of rotation, lines of curvature, sectional curvature.

MSC: 53B25.

Received: 14.12.2017
Revised: 06.06.2018

Language: English

DOI: 10.15407/mag15.02.192



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© Steklov Math. Inst. of RAS, 2025