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arXiv · 1905.11205

Curves on a smooth surface with position vectors lie in the tangent plane

Absos Ali Shaikh·Pinaki Ranjan Ghosh
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Abstract

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.

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Absos Ali Shaikh, Pinaki Ranjan Ghosh. 2019-05-21. Curves on a smooth surface with position vectors lie in the tangent plane. https://arxiv.org/abs/1905.11205

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