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 T₁, P₁, U₁. Furthermore, we compute the deviations of the position vector of the normal curve on regular surfaces along the unit tangent vector T₁, the unit normal U₁ perpendicular to the oriented surface, and the cross product of U₁ and T₁ due to isometric transformations.
Shaikh et al. (Wed,) studied this question.