Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 3, pp. 364-371   https://doi.org/10.15407/mag16.03.364     ( to contents , go back )
https://doi.org/10.15407/mag16.03.364

On Projective Classification of Points of a Submanifold in the Euclidean Space

Alexander Yampolsky

V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61022, Ukraine
E-mail: a.yampolsky@karazin.ua

Received June 1, 2020.

Abstract

We propose the classification of points of a submanifold in the Euclidean space in terms of the indicatrix of normal curvature up to projective trans- formation and give a necessary condition for finiteness of number of such classes. We apply the condition to the case of three-dimensional submani- fold in six-dimensional Euclidean space and prove that there are 10 types of projectively equivalent points.

Mathematics Subject Classification 2000: 53A07, 53B20, 53B25
Key words: normal curvature indicatrix, submanifold point type, projective transformation

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