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Developable surfaces along frontal curves on embedded surfaces

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Abstract

We consider two types of developable surfaces along a frontal curve on an embedded surface in the Euclidean 3-space. One is called the osculating developable surface, and the other is called the normal developable surface. The frontal curve may have singular points. We give new invariants of the frontal curve which characterize singularities of the developable surfaces. Moreover, a frontal curve is a contour generator with respect to an orthogonal projection or a central projection if and only if one of these invariants is constantly equal to zero.

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Authors and Affiliations

  1. Education and Research Center for Mathematical and Data Science, Hokkaido University, Kita 12, Nishi 7, Kita-Ku, Sapporo, Hokkaido, 060-0812, Japan

    Shun’ichi Honda

  2. Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

    Shyuichi Izumiya

  3. Muroran Institute of Technology, Muroran, 050-8585, Japan

    Masatomo Takahashi

Authors
  1. Shun’ichi Honda
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  2. Shyuichi Izumiya
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  3. Masatomo Takahashi
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Correspondence to Shun’ichi Honda.

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This work was supported by JSPS KAKENHI Grant Numbers JP26247006, JP17K05238.

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Honda, S., Izumiya, S. & Takahashi, M. Developable surfaces along frontal curves on embedded surfaces. J. Geom. 110, 27 (2019). https://doi.org/10.1007/s00022-019-0485-z

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  • DOI: https://doi.org/10.1007/s00022-019-0485-z

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