Helix preserving mappings

Abstract

In this study, we define two types of mappings that preserve the constant angle between the tangent vector field and the axis of a given helix in Euclidean spaces. The first type generates helices in the n-dimensional Euclidean space from helices in the same space. The second type generates helices in the (n+1)-dimensional Euclidean space from helices in the n-dimensional Euclidean space. In addition, we give invariants of these mappings and study polynomial, rational, conical, ellipsoidal, and hyperboloidal helices supported by examples. © 2020 John Wiley & Sons, Ltd.