Focal representation of k-slant Helices in E^m+1

The focal representation of a generic regular curve γ in E^m+1 consists of the centers of the osculating hyperplanes. A k-slant helix γ in E^m+1 is a (generic) regular curve whose unit normal vector V_k makes a constant angle with a fixed direction in E^m+1. In the present paper we proved that if γ is a k-slant helix in E^m+1, then the focal representation C_γ of γ in E^m+1 is an (m− k + 2)-slant helix in E^m+1.