Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 15 (2020), 459 -- 470

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This work is licensed under a Creative Commons Attribution 4.0 International License.

ON SOME SPECIAL CURVES IN LORENTZ-MINKOWSKI PLANE

Ali Uçum, Kazım İlarslan and Ivaïlo M. Mladenov

Abstract. Here we consider the plane curves whose curvature κ depends on the distance from the origin in Lorentz-Minkowski plane 𝔼12. We obtain their explicit parameterizations in the cases when the plane curves have curvatures which are linear or quadratic functions of the distance of their points from the origin in 𝔼12 up to a real positive multiplier σ ∈ ℝ+.
We have derived also the algebraic equations which are uniformized by these parameterziations.

2020 Mathematics Subject Classification: 53C40; 53C50
Keywords: Curvature, plane curves, Lorentz-Minkowski plane

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Ali Uçum
Kırıkkale University, Faculty of Sciences and Arts
Department of Mathematics,
Kırıkkale, Turkey.
e-mail: aliucum05@gmail.com


Kazım İlarslan
Kırıkkale University, Faculty of Sciences and Arts
Department of Mathematics,
Kirıkkale, Turkey.
e-mail: kilarslan@yahoo.com

Ivaïlo M. Mladenov
Institute of Biophysics & Biomedical Engineering
Bulgarian Academy of Sciences, Sofia, Bulgaria.
e-mail: mladenov@bio21.bas.bg

http://www.utgjiu.ro/math/sma