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

2013/05/10 by Günay Öztürk, Betül Bulca, Ozturk, Gunay +5
Computer Science · Mathematics · #53A04 #53C42 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1305.2337

openalex publication_date 2013/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Some Characterizations of Cylindrical Helices in Eⁿ

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