Focal representation of k-slant helices in Em+1

Abstract

The focal representation of a generic regular curve gamma in Em+1 consists of the centers of the osculating hyperplanes. A k-slant helix gamma in Em+1 is a (generic) regular curve whose unit normal vector V-k makes a constant angle with a fixed direction (U) over right arrow in Em+1. In the present paper we proved that if gamma is a k-slant helix in Em+1, then the focal representation C-gamma of gamma in Em+1 is an (m - k + 2)-slant helix in Em+1.