Abstract
This paper mainly focuses on some notions of the lightlike rectifying curves and the centrodes in Minkowski 3-space. Some geometrical characteristics of the three types of lightlike curves are obtained. In addition, we obtain the conditions of the centrodes of the lightlike curves are the lightlike rectifying curves. Meanwhile, a detailed analysis between the N-type lightlike slant helices and the centrodes of lightlike curves is provided in this paper. We give the projections of the lightlike rectifying curves to the timelike planes.
Highlights
Despite its long history, curve theory is still one of the most important interesting topics in differential geometry [1,2,3,4,5,6,7,8,9,10,11]
We organize the present manuscript as follows: the second section contains the basic notions of Minkowski 3-space and the Frenet frame of a lightlike curve in R31
This paper considered the geometrical properties of three types of lightlike curves in Minkowski 3-space
Summary
Curve theory is still one of the most important interesting topics in differential geometry [1,2,3,4,5,6,7,8,9,10,11]. The relationship between a non-lightlike rectifying curve and the centrode of a non-lightlike curve was given in [5,12]. We pursue and describe the geometrical characteristics of lightlike rectifying curves in Minkowski 3-space. We organize the present manuscript as follows: the second section contains the basic notions of Minkowski 3-space and the Frenet frame of a lightlike curve in R31. The main conclusions (Theorems 1 and 4) describe the geometrical properties of the lightlike rectifying curves.
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