Spinor Darboux Equations of Curves in Euclidean 3-Space
\.Il\.Im K\.I\c{S}\.I, Murat Tosun
TL;DR
This paper introduces a spinor formulation for the Darboux frame on surfaces in Euclidean 3-space and explores its relation to the Frenet frame, providing a new mathematical perspective.
Contribution
It presents a novel spinor-based approach to Darboux frames and connects it with the Frenet frame in Euclidean 3-space.
Findings
Established the spinor formulation of Darboux frames.
Derived relations between spinor Darboux and Frenet frames.
Abstract
In this paper, the spinor formulation of Darboux frame on an oriented surface is given. Also, the relation between the spinor formulation of Frenet frame and Darboux frame are obtained.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Advanced Mathematical Modeling in Engineering · Geometric Analysis and Curvature Flows