Startseite Mathematik Envelopes of circles and spacelike curves in the Lorentz–Minkowski 3-space
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Envelopes of circles and spacelike curves in the Lorentz–Minkowski 3-space

  • Rui Pacheco ORCID logo EMAIL logo und Susana D. Santos ORCID logo
Veröffentlicht/Copyright: 11. Februar 2020

Abstract

The isotropy projection establishes a correspondence between curves in the Lorentz–Minkowski space 𝐄13 and families of cycles in the Euclidean plane (i.e., curves in the Laguerre plane 2). In this paper, we shall give necessary and sufficient conditions for two given families of cycles to be related by a (extended) Laguerre transformation in terms of the well known Lorentzian invariants for smooth curves in 𝐄13. We shall discuss the causal character of the second derivative of unit speed spacelike curves in 𝐄13 in terms of the geometry of the corresponding families of oriented circles and their envelopes. Several families of circles whose envelopes are well-known plane curves are investigated and their Laguerre invariants computed.


Communicated by Anna Wienhard


Award Identifier / Grant number: UID/MAT/00212/2019

Award Identifier / Grant number: UID/MAT/04561/2019

Funding statement: The authors were partially supported by National Funding from FCT – Fundação para a Ciência e a Tecnologia, under the projects UID/MAT/00212/2019 and UID/MAT/04561/2019.

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Received: 2019-04-08
Revised: 2019-10-31
Published Online: 2020-02-11
Published in Print: 2020-05-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 4.2.2026 von https://www.degruyterbrill.com/document/doi/10.1515/forum-2019-0092/pdf
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