A focal representation of a generic regular curve { \gamma} in E^{ m+1} consists of the centers of the osculating hyperplanes. A k-slant helix { \gamma} in E^{ m+1} is a (generic) regular curve whose unit normal vector V_{ k} makes a constant angle with a fixed direction U in E^{ m+1}. In the present paper we proved that if { \gamma} is a k-slant helix in E^{ m+1}, then the focal representation C_{ { \gamma}} of { \gamma} in E^{ m+1} is a (m-k+2)-slant helix in E^{ m+1}.
Categories: math.DG