Generic Properties of Framed Rectifying Curves

Wang, Yongqiao; Pei, Donghe; Gao, Ruimei

doi:10.3390/math7010037

Cited by 23 publications

(55 citation statements)

References 12 publications

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“…Motivated by the achievements of Chen on rectifying curves, a series of further research works were carried out in different space-times by many mathematicians [2][3][4]. For instance, the rectifying curves are generalized into the ones in Minkowski 3-space, which are divided into space-like (resp.…”

Section: Introductionmentioning

confidence: 99%

Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space

Qian

Yin

et al. 2021

Mathematics

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In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. Meanwhile, the rectifying isotropic curves are expressed by the Bessel functions explicitly. Last but not least, the centrodes of rectifying isotropic curves are explored in detail.

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Section: Introductionmentioning

confidence: 99%

Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space

Qian

Yin

et al. 2021

Mathematics

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“…This is not only the promotion of Frenet curves but also the promotion of Legendre curves [14]. Subsequently, using the framed curve as a tool, some authors have studied geometric objects in different spaces [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Nullcone Fronts of Spacelike Framed Curves in Minkowski 3-Space

Pei

2021

Mathematics

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The investigation of objects in Minkowski space is of great significance, especially for those objects with mathematical and physical backgrounds. In this paper, we study nullcone fronts, which are formed by the light rays emitted from points on a spacelike curve. However, if the spacelike curve is singular, then we cannot use the usual tools and methods to study related issues. To solve these problems, we show the definition of spacelike framed curves in Minkowski 3-space, whose original curves may contain singularities. Then, the singularities of the nullcone fronts are characterized by using framed curvatures of spacelike framed curves. Finally, we exhibit some examples to illustrate our results.

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“…Moreover, Wang et. al obtained a moving adapted frame to investigate the properties of rectifying curve with singular points in R 3 , and this frame was used to analyze some special curves with singular points [2]. For more details on the notion of framed curves, see [3]- [9].…”

Section: Introductionmentioning

confidence: 99%

On the Framed Normal Curves in Euclidean 4-space

Yıldız

Akyiğit

2021

Fundamental Journal of Mathematics and Applications

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In this paper, we introduce the adapted frame of framed curves and we give the relations between the adapted frame and Frenet type frame of the framed curve in four-dimensional Euclidean space. Moreover, we define the framed normal curves in four-dimensional Euclidean space. We obtain some characterizations of framed normal curves in terms of their framed curvature functions. Furthermore, we give the necessary and sufficient condition for a framed curve to be a framed normal curve.

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Generic Properties of Framed Rectifying Curves

Cited by 23 publications

References 12 publications

Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space

Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space

Nullcone Fronts of Spacelike Framed Curves in Minkowski 3-Space

On the Framed Normal Curves in Euclidean 4-space

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