Characterization of Dual Spacelike Curves on Dual Lightlike Cone Q~2 Utilizing the Structure Function
Year: 2024
Type: article
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 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.
Source: Symmetry
DOI: 10.3390/sym16121574
Authors: Pınar Balkı Okullu, Hasan Hüseyin Uğurlu
Institutions: Manisa Celal Bayar University, Gazi University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
OpenAlex ID: W4404671372