On the Structure of Multidimensional
Submanifolds with Metric of Revolution in
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
Received December 14, 2017, revised June 6, 2018.
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.