Naslov
Involutes of Pseudo-Null Curves in Lorentz- Minkowski 3-Space

Autori
Lopez, Rafael ; Milin Šipuš, Željka ; Primorac Gajčić, Ljiljana ; Protrka, Ivana

Izvornik
Mathematics (2227-7390) 9 (2021), 11; 1256, 14

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Lorentz-Minkowski space ; pseudo-null curve ; involute ; null curve

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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