Curves on a smooth surface with position vectors lie in the tangent plane
General Mathematics
2019-05-28 v1
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.
Keywords
Cite
@article{arxiv.1905.11205,
title = {Curves on a smooth surface with position vectors lie in the tangent plane},
author = {Absos Ali Shaikh and Pinaki Ranjan Ghosh},
journal= {arXiv preprint arXiv:1905.11205},
year = {2019}
}
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9 pages