Special Smarandache Curves with Respect to Darboux Frame in the Galilean 3-Space
Tevfik \c{S}ahin, Merve Okur
TL;DR
This paper studies special Smarandache curves related to the Darboux frame on surfaces within Galilean 3-space, providing explicit formulas and examples for various types of curves such as geodesic and asymptotic.
Contribution
It introduces explicit formulas for special Smarandache curves with respect to the Darboux frame in Galilean 3-space, including examples for different curve types.
Findings
Explicit formulas for Smarandache curves in G3
Characterization of geodesic, asymptotic, and curvature lines
Examples illustrating the theoretical results
Abstract
In the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3. Furthermore, we give general position vectors of special Smarandache curves of geodesic, asymptotic and curvature line on the surface in G3. As a result of this, we provide some related examples of these curves.
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Taxonomy
TopicsMathematics and Applications · Advanced Numerical Analysis Techniques · Advanced Differential Geometry Research