Geometric invariants of normal curves under conformal transformation in\n \𝔼³

2019/07/12 by Mohamd Saleem Lone, Lone, Mohamd Saleem
Mathematics · #53A04 #53A05 #53A15 #Algebraic Geometry and Number Theory #FOS: Mathematics #General Mathematics (math.GM) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1908.03527

openalex publication_date 2019/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the geometric invariant properties of a normal\ncurve on a smooth immersed surface under conformal transformation. We obtain an\ninvariant-sufficient condition for the conformal image of a normal curve. We\nalso find the deviations of normal and tangential components of the normal\ncurve under the same motion. The results in cite9 are claimed as special\ncases of this paper.\n

Related

• Normal curves on a smooth immersed surface
• Rectifying curves under conformal transformation
• Conformal invariants of curves via those for inscribed polygons with circular edges
• Generalized Normal Ruled Surface of a Curve in the Euclidean 3-space
• Rectifying curves on a smooth surface immersed in the euclidean space