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Dualities and envelopes of one‐parameter families of frontals in hyperbolic and de Sitter 2‐spaces

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  • L. Chen
  • D. H. Pei
  • M. Takahashi

Abstract

We consider envelopes of one‐parameter families of frontals in hyperbolic and de Sitter 2‐space from the viewpoint of duality, respectively. Since the classical notions of envelopes for singular curves do not work, we have to find a new method to define the envelope for singular curves in hyperbolic space or de Sitter space. To do that, we first introduce notions of one‐parameter families of Legendrian curves by using the Legendrian dualities. Afterwards, we give definitions of envelopes for the one‐parameter families of frontals in hyperbolic and de Sitter 2‐space, respectively. We investigate properties of the envelopes. At last, we give relationships among those envelopes.

Suggested Citation

  • L. Chen & D. H. Pei & M. Takahashi, 2020. "Dualities and envelopes of one‐parameter families of frontals in hyperbolic and de Sitter 2‐spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 893-909, May.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:5:p:893-909
    DOI: 10.1002/mana.201800316
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