In this paper, we are investigating that under which conditions of the geodesic curvature of unit speed curve γ that lies on the unit sphere, the curve c which is obtained by using γ, is a spherical helix or slant helix.
In this work, we study timelike rectifying slant helices in E 3 1. First, we find general equations of the curvature and the torsion of timelike rectifying slant helices. After that, by solving second order linear differential equations, we obtain families of timelike rectifying slant helices that lie on cones.
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.
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