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Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers by Ildefonso Castro; Ildefonso Castro-Infantes; Jesús Castro-Infantes is a Mathematics article available to read on EtoBox.

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This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane L whose curvature is expressed in terms of the Lorentzian pseudodistance to xed geodesics. In this way, we get a complete description of all the elastic curves in L and provide the Lorentzian versions of catenaries and grimreaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically.

Who reads Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers?

Author

Ildefonso Castro; Ildefonso Castro-Infantes; Jesús Castro-Infantes

Publisher

Walter de Gruyter GmbH

Published

2018

Language

EN

Field

Mathematics (Physical Sciences)