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Ruled invariants and associated ruled surfaces of a space curve

Author

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  • Liu, Huili
  • Liu, Yixuan
  • Jung, Seoung Dal

Abstract

As we know, a ruled surface is the tangent ruled surface of a space curve if and only if its ruled distance density function vanishes identically; a ruled surface is the binormal ruled surface of a space curve if and only if its ruled translation density function vanishes identically. The ruled distance density function and translation density function are differential invariants of ruled surfaces in three dimensional Euclidean space. In this paper we give the necessary and sufficient condition of which a ruled surface is the principal normal ruled surface of a space curve using the theories of ruled invariants of ruled surface in three dimensional Euclidean space.

Suggested Citation

  • Liu, Huili & Liu, Yixuan & Jung, Seoung Dal, 2019. "Ruled invariants and associated ruled surfaces of a space curve," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 479-486.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:479-486
    DOI: 10.1016/j.amc.2018.12.011
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    Cited by:

    1. Jie Huang & Donghe Pei, 2019. "Singularities of Non-Developable Surfaces in Three-Dimensional Euclidean Space," Mathematics, MDPI, vol. 7(11), pages 1-11, November.

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