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<p>In this paper, we consider two kinds of ruled surfaces along a spacelike curve lying in a lightcone in Minkowski 3-space, the timelike ruled surfaces and the lightlike ruled surfaces. Meanwhile, we also consider two curves generated by such a spacelike curve. As an extension and an application of the unfolding theory in singularity theory, we complete the classifications of the singular points of these two ruled surfaces and two curves. In addition, the study shows that the differential geometric invariant of spacelike curves measured the order of contact between spacelike curves and plane curves. Finally, an example is provided to illustrate our theoretical results.</p>

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Ruled surfaces along spacelike curves on lightcone in Minkowski 3-space

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Jiakun Jiang,
  • Donghe Pei

摘要

In this paper, we consider two kinds of ruled surfaces along a spacelike curve lying in a lightcone in Minkowski 3-space, the timelike ruled surfaces and the lightlike ruled surfaces. Meanwhile, we also consider two curves generated by such a spacelike curve. As an extension and an application of the unfolding theory in singularity theory, we complete the classifications of the singular points of these two ruled surfaces and two curves. In addition, the study shows that the differential geometric invariant of spacelike curves measured the order of contact between spacelike curves and plane curves. Finally, an example is provided to illustrate our theoretical results.