Involutes of Pseudo-Null Curves in Lorentz–Minkowski 3-Space
Metadatos
Mostrar el registro completo del ítemAutor
López Camino, RafaelEditorial
MDPI
Materia
Lorentz–Minkowski 3-space Pseudo-null curve Social Involution Null curve
Fecha
2021Referencia bibliográfica
López, R.; Milin Šipuš, Ž.; Primorac Gajˇci´c, L.; Protrka, I. Involutes of Pseudo-Null Curves in Lorentz–Minkowski 3-Space. Mathematics 2021, 9, 1256. https:// doi.org/10.3390/math9111256
Patrocinador
MTM2017-89677-P, MINECO/ AEI/FEDER, UE.Resumen
In this paper, we analyze involutes of pseudo-null curves in Lorentz–Minkowski 3-space.
Pseudo-null curves are spacelike curves with null principal normals, and their involutes can be
defined analogously as for the Euclidean curves, but they exhibit properties that cannot occur in
Euclidean space. The first result of the paper is that the involutes of pseudo-null curves are null
curves, more precisely, null straight lines. Furthermore, a method of reconstruction of a pseudo-null
curve from a given null straight line as its involute is provided. Such a reconstruction process in
Euclidean plane generates an evolute of a curve, however it cannot be applied to a straight line. In
the case presented, the process is additionally affected by a choice of different null frames that every
null curve allows (in this case, a null straight line). Nevertheless, we proved that for different null
frames, the obtained pseudo-null curves are congruent. Examples that verify presented results are
also given.