Some Characterizations of Cylindrical Helices in Eⁿ

2009/01/21 by Ahmad T. Ali, Ali, Ahmad T., López, Rafael · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Mathematics and Applications #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.0901.3325

Abstract

We consider a unit speed curve α in Euclidean n-dimensional space Eⁿ and denote the Frenet frame by \v₁,...,v_n\. We say that α is a cylindrical helix if its tangent vector v₁ makes a constant angle with a fixed direction U. In this work we give different characterizations of such curves in terms of their curvatures.

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