Focal Representation of k-slant Helices in Eᵐ⁺¹

الأصل · EN

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