The present paper deals with a study of curves on a smooth surface whose position vector always lies in the tangent plane of the surface and it is proved that such curves remain invariant under isometry of surfaces. It is also shown that length of the position vector, tangential component of the position vector and geodesic curvature of a curve on a surface whose position vector always lies in the tangent plane are invariant under isometry of surfaces.

中文翻译：

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位置向量位于切平面中的光滑表面上的曲线

本文研究了光滑曲面上的曲线，该曲面的位置矢量始终位于曲面的切平面上，并证明了在曲面等轴测情况下，此类曲线保持不变。还表明位置矢量的长度，位置矢量的切向分量和位置矢量始终位于切线平面上的曲面上的曲线的测地曲率在表面等轴测图中是不变的。