Geometry of evolutoids and pedaloids for curves on timelike surfaces
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Published:2023-12-16
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Volume:
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ISSN:0219-8878
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Container-title:International Journal of Geometric Methods in Modern Physics
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language:en
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Short-container-title:Int. J. Geom. Methods Mod. Phys.
Author:
Hua Yuefeng1ORCID,
Liu Haiming1ORCID
Affiliation:
1. School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, P. R. China
Abstract
In this paper, we focus on geometry of evolutoids and pedaloids for timelike curves and spacelike curves on timelike surfaces. First, by studying an example of a pseudo-circle, we get some properties of timelike curve on timelike surface. Then, we introduce a moving frame along curves and describe the corresponding evolutoids of curves as ruled surfaces. After that, we investigate relationships between pedal surfaces of evolutoids and pedaloids of curves. Moreover, we investigate the singularities of the evolutoids and the pedaloids.
Funder
the Project of Science and Technology of Mudanjiang Normal University
the Natural Science Foundation of Heilongjiang Province of China
Project of Science and Technology of Heilongjiang Provincial Education Department
Publisher
World Scientific Pub Co Pte Ltd
Subject
Physics and Astronomy (miscellaneous)