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On evolutes of curves in the isotropic plane

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Abstract

We associate to each spacelike curve in the isotropic plane a null curve in the Lorentzian 3-space. We relate the isotropic geometry of the first to the Lorentzian geometry of the second. We prove a version of the Tait–Kneser theorem for curves in the isotropic plane. Some explicit examples are given.

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Funding

The authors were partially supported by Fundação para a Ciência e Tecnologia through the projects UIDB/00212/2020 (https://doi.org/10.54499/UIDB/00212/2020) and UIDB/04561/2020 (https://doi.org/10.54499/UIDB/04561/2020).

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Authors and Affiliations

  1. Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, 6201-001, Covilhã, Portugal

    R. Pacheco

  2. Centro de Matemática, Aplicações Fundamentais e Investigação Operacional and Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016, Lisbon, Portugal

    S. D. Santos

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  1. R. Pacheco
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  2. S. D. Santos
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Both authors discussed and developed the theory, wrote and revised the manuscript.

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Correspondence to R. Pacheco.

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Pacheco, R., Santos, S.D. On evolutes of curves in the isotropic plane. Aequat. Math. (2024). https://doi.org/10.1007/s00010-024-01086-w

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  • DOI: https://doi.org/10.1007/s00010-024-01086-w

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