On projective classification of points of a submanifold in the Euclidean space

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