Involutes of null Cartan curves and their representations in Minkowski 3-space

Qian, Jinhua; Sun, Mingyu; Zhang, Bo

doi:10.1007/s00500-023-08848-9

Cited by 2 publications

(1 citation statement)

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“…The basic properties of involute evolute curves for unit speed curves in Euclidean space were investigated by C ¸alışkan and Bilici [15]. In addition, this pair of curves has been extensively studied in different spaces and using different frames [16][17][18][19]. In this paper, our aim is to generate the solutions of LIE using the Frenet frame of involute-evolute curve pairs and discuss the geometric properties of the surfaces corresponding to solutions of LIE.…”

Section: Introductionmentioning

confidence: 99%

Solutions of localized induction equation associated with involute–evolute curve pair

Eren,

Myrzakulova,

Ersoy

et al. 2023

Soft Comput

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In this paper, we derive the surfaces, which are called Hasimoto surfaces, corresponding to solutions of the localized induction equation for involute evolute curves. We investigate the differential geometric properties of these surfaces associated with the involute evolute curves. Moreover, we calculate the Gaussian and mean curvatures of Hasimoto surfaces in terms of curvatures of the curve pairs. Then, we determine the conditions for these surfaces' parameter curves to be the geodesics, asymptotics, and/or lines of curvature of the surface. We have demonstrated the evolutions of involute evolute curves in examples.

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Section: Introductionmentioning

confidence: 99%