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Behavior of principal curvatures of frontals near non-front singular points and their applications

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Abstract

We investigate behavior of principal curvatures and principal vectors near a non-degenerate singular point of the first kind of frontals. As an application, we extend the notion of Ribaucour transformations to frontals with singular points.

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Acknowledgements

The authors thank Joseph Cho, Mason Pember and Gudrun Szewieczek for fruitful advices, and Maho Ichikawa for helping calculations about Ribaucour transformations of surfaces of revolution.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Kobe University, Rokko 1-1, Kobe, 657-8501, Japan

    Kentaro Saji

  2. Department of Mathematics, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan

    Keisuke Teramoto

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  1. Kentaro Saji
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  2. Keisuke Teramoto
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Correspondence to Kentaro Saji.

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The authors were partially supported by JSPS KAKENHI Grant Numbers JP18K03301 and JP19K14533, and CAPES/JSPS Bilateral Joint Research Project.

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Saji, K., Teramoto, K. Behavior of principal curvatures of frontals near non-front singular points and their applications. J. Geom. 112, 39 (2021). https://doi.org/10.1007/s00022-021-00605-3

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  • DOI: https://doi.org/10.1007/s00022-021-00605-3

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