Abstract
A 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 U 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 a (m-k+2)-slant helix in E^{m+1}.
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