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Keywords = dual lightlike cone

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13 pages, 1247 KB  
Article
Characterization of Dual Spacelike Curves on Dual Lightlike Cone Q~2 Utilizing the Structure Function
by Pınar Balkı Okullu and Hasan Hüseyin Uğurlu
Symmetry 2024, 16(12), 1574; https://doi.org/10.3390/sym16121574 - 25 Nov 2024
Cited by 1 | Viewed by 941
Abstract
This study is about the dual spacelike curves lying on the dual lightlike cone, which can be either symmetric or asymmetric. We first establish the dual associated curve, which is related to the reference curve. Using these curves and the derivative of the [...] Read more.
This study is about the dual spacelike curves lying on the dual lightlike cone, which can be either symmetric or asymmetric. We first establish the dual associated curve, which is related to the reference curve. Using these curves and the derivative of the reference curve, we derive the dual asymptotic orthonormal frame. Next, we define the dual structure function, curvature function, and Frenet formulae, and express the curvature function in terms of the dual structure function. This leads to a differential equation that characterizes the dual cone curve in relation to its curvature function. Since curves with constant curvature maintain the same curvature at every point, their geometry is more predictable. Therefore, we assume that the dual cone curvature function is constant and examine how this condition affects the behavior and geometric properties of the dual curves. As a result of this investigation, some new results and definitions are obtained. Full article
(This article belongs to the Special Issue Symmetry in Differential Geometry and Geometric Analysis)
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