The present paper deals with some characterizations of rectifying and osculating curves on a smooth surface with respect to the reference frame $\{\overrightarrow{T},\overrightarrow{N},\overrightarrow{T}\times \overrightarrow{N}\}$. We have computed the components of position vectors of rectifying and osculating curves along $\overrightarrow{T},\overrightarrow{N},\overrightarrow{T}\times \overrightarrow{N}$ and then investigated their invariancy under isometry of surfaces, and it is shown that they are invariant iff either the normal curvature of the curve is invariant or the position vector of the curve is in the direction of the tangent vector to the curve.

中文翻译：

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光滑浸没面上整流和密切曲线的一些表征

本文讨论了相对于参考系的光滑表面上的校正和密切曲线的一些表征 $\{\overrightarrow{吨},\overrightarrow{N},\overrightarrow{吨}\times \overrightarrow{N}\}$. 我们已经计算了整流曲线和密切曲线的位置向量的分量$\overrightarrow{吨},\overrightarrow{N},\overrightarrow{吨}\times \overrightarrow{N}$ 然后研究了它们在曲面等距下的不变性，结果表明，当曲线的法向曲率不变或曲线的位置向量在曲线的切向量的方向上时，它们是不变的。