A review on the Vn-slant helices in lightlike cone Qn+1 En+2
Fatma Almaz, Handan Oztekin
TL;DR
This paper explores the properties and characterizations of Vn-slant helices within lightlike cones in higher-dimensional spaces, providing differential equations and conditions for their geometric behavior.
Contribution
It introduces the harmonic curvature functions of Vn-slant helices and derives differential equations and conditions using asymptotic orthonormal frames in lightlike cones.
Findings
Differential equations for harmonic curvature functions of Vn-slant helices.
Necessary and sufficient conditions for Vn-slant helices in lightlike cones.
Use of asymptotic orthonormal frames to characterize Vn-slant helices.
Abstract
In this paper, Vn-slant helices and the harmonic curvature functions of Vn-slant helices are de ned in lightlike cone Qn+1, and the differential equations of the harmonic curvature functions Hi, 1<i<n-2 of Vn-slant helices are expressed by using constant vector field W that is the axis of Vn slant helices. Also, the necessary and sufficient conditions are given according to the condition of being Vn-slant helices by using the asymptotic orthonormal frame in Qn+1.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Waves and Solitons · Black Holes and Theoretical Physics