Some characterizations of normal curves under isometry using Darboux frame

This paper deals with the study of characterizations of a normal curve in 3-dimensional Euclidean space and presents a sufficient condition for the invariance of a normal curve on regular surfaces under isometric transformations using the Darboux frame { T_1 , P_1 , U_1 }. Furthermore, we compute the deviations of the position vector of the normal curve on regular surfaces along the unit tangent vector T_1 , the unit normal U_1 perpendicular to the oriented surface, and the cross product of U_1 and T_1 due to isometric transformations.