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Dualities and envelopes of one‐parameter families of frontals in hyperbolic and de Sitter 2‐spaces
Author(s) -
Chen L.,
Pei D. H.,
Takahashi M.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800316
Subject(s) - mathematics , envelope (radar) , duality (order theory) , space (punctuation) , de sitter universe , parameter space , de sitter space , pure mathematics , mathematical analysis , geometry , physics , universe , computer science , quantum mechanics , telecommunications , radar , operating system
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.