Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane
In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="double-struck">R</...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/6f577548fab343478590c9f9824c734a |
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| Sumario: | In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="double-struck">R</mi><mn>1</mn><mn>2</mn></msubsup></semantics></math></inline-formula>. The pedal curve is always given by the pseudo-orthogonal projection of a fixed point on the tangent lines of the base curve. For a mixed-type curve, the pedal curve at lightlike points cannot always be defined. Herein, we investigate when the pedal curves of a mixed-type curve can be defined and define the pedal curves of the mixed-type curve using the lightcone frame. Then, we consider when the pedal curves of the mixed-type curve have singular points. We also investigate the relationship of the type of the points on the pedal curves and the type of the points on the base curve. |
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