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arXiv · 2104.02907

Some characterizations of rectifying curves on a smooth surface in Euclidean 3-space

Akhilesh Yadav·Buddhadev Pal
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Abstract

In this paper, we investigate sufficient condition for the invariance of a rectifying curve on a smooth surface immersed in Euclidean 3-space under isometry by using Darboux frame $\left\lbrace T, P, U\right\rbrace$. Further, we find the deviations of the position vector of a rectifying curve on the smooth surface along any tangent vector $T = a\phi_u + b\phi_v$ with respect to the isometry. We also find the deviations of the position vector of a rectifying curve on the smooth surface along the unit normal $U$ to the surface and along $P (= U \times T)$ with respect to the isometry.

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Akhilesh Yadav, Buddhadev Pal. 2021-04-07. Some characterizations of rectifying curves on a smooth surface in Euclidean 3-space. https://arxiv.org/abs/2104.02907

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