Abstract
In this study, spinor representations of the curves on surfaces have been expressed via B-Darboux frame in Euclidean space E^3. The relation between Darboux and B-Darboux frame has been established according to their spinor formulations. Moreover, all these spinor characterizations have been interpreted in the meaning of Darboux frame (via the curvatures) in Euclidean 3-space. Finally, an application has been presented about the characterizations of the relations between the B-Darboux frame and the spinors.
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