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

2021/04/07 by Akhilesh Yadav, Yadav, Akhilesh, Buddhadev Pal +1
Mathematics · #53A04 #53A05 #53A15 #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2104.02907

openalex publication_date 2021/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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 \lbrace T, P, U\rbrace. Further, we find the deviations of the position vector of a rectifying curve on the smooth surface along any tangent vector T = aϕ_u + bϕ_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 × T) with respect to the isometry.

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