Abstract
In this paper, we introduce a new frame which is called the B‐Darboux frame on a surface in Euclidean 3‐space. We know that the parallel transport frame is derived from the Frenet frame along a space curve on a surface. Analogously, we derive the B‐Darboux frame from the Darboux frame along a space curve on a surface in Euclidean 3‐space. Then, we obtain the intrinsic equations due to the B‐Darboux frame for a generalized relaxed elastic line on an oriented surface and give some applications of this obtained results in Euclidean 3‐space.
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