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- Title
Envelopes of circles and spacelike curves in the Lorentz-Minkowski 3-space.
- Authors
Pacheco, Rui; Santos, Susana D.
- Abstract
The isotropy projection establishes a correspondence between curves in the Lorentz-Minkowski space E³1 and families of cycles in the Euclidean plane (i.e., curves in the Laguerre plane L2). 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 E³1. We shall discuss the causal character of the second derivative of unit speed spacelike curves in E³1 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.
- Subjects
CURVES; LAGUERRE geometry; LORENTZ spaces; CIRCLE; MINKOWSKI space; PLANE curves; GEOMETRY
- Publication
Forum Mathematicum, 2020, Vol 32, Issue 3, p693
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2019-0092