2024
DOI: 10.3934/math.2024635
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Characterization of imbricate-ruled surfaces via rotation-minimizing Darboux frame in Minkowski 3-space $ \mathrm{E}_1^3 $

Emad Solouma,
Ibrahim Al-Dayel,
Meraj Ali Khan
et al.

Abstract: <abstract><p>Using a common tangent vector field to a surface along a curve, in this study we discussed a new Darboux frame that we referred to as the rotation-minimizing Darboux frame (RMDF) in Minkowski 3-space. The parametric equation resulting from the RMDF frame for an imbricate-ruled surface was then provided. As a result, minimal (or maximal for timelike surfaces) ruled surfaces were derived, along with the necessary and sufficient criteria for imbricate-ruled surfaces to be developable. The… Show more

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