On the equiform geometry of special curves in hyperbolic and de Sitter planes

A. A. Abdel-Salam; M. I. Elashiry; M. Khalifa Saad; A. A. Abdel-Salam; M. I. Elashiry; M. Khalifa Saad

doi:10.3934/math.2023937

AIMS Mathematics

2023, Volume 8, Issue 8: 18435-18454. doi: 10.3934/math.2023937

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On the equiform geometry of special curves in hyperbolic and de Sitter planes

1.
Department of Mathematics, Faculty of Science and Arts, Northern Border University, Rafha, KSA
2.
Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, Egypt
3.
Department of Mathematics, Faculty of Science, Fayoum University, El-Fayoum, Egypt
4.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA

Received: 13 March 2023 Revised: 10 May 2023 Accepted: 23 May 2023 Published: 30 May 2023
MSC : 35Q51, 51B20, 53A35, 76B47

In this paper, we aim to investigate the equiform differential geometric properties of the evolute and involute frontal curves in the hyperbolic and de Sitter planes. We inspect the relevance between evolute and involute frontal curves that relate to symmetry properties. Also, under the viewpoint of symmetry, we expand these notions to the frontal curves. Moreover, we look at the classification of these curves and introduce the notion of frontalisation for its singularities. Finally, we provide two numerical examples with drawing as an application, through which we authenticate our theoretical results.
- hyperbolic plane,
- de Sitter plane,
- evolute curve,
- involute curve,
- frontal curves
Citation: A. A. Abdel-Salam, M. I. Elashiry, M. Khalifa Saad. On the equiform geometry of special curves in hyperbolic and de Sitter planes[J]. AIMS Mathematics, 2023, 8(8): 18435-18454. doi: 10.3934/math.2023937

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Abstract

In this paper, we aim to investigate the equiform differential geometric properties of the evolute and involute frontal curves in the hyperbolic and de Sitter planes. We inspect the relevance between evolute and involute frontal curves that relate to symmetry properties. Also, under the viewpoint of symmetry, we expand these notions to the frontal curves. Moreover, we look at the classification of these curves and introduce the notion of frontalisation for its singularities. Finally, we provide two numerical examples with drawing as an application, through which we authenticate our theoretical results.

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