Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 3, pp. 364-371     ( to contents , go back )

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

Received June 1, 2020.


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 2010: 53A07, 53B20, 53B25
Key words: normal curvature indicatrix, submanifold point type, projective transformation

Download 702600 byte View Contents