Geometry of tubular surfaces and their focal surfaces in Euclidean 3-space

M. Khalifa Saad; Nural Yüksel; Nurdan Oğraş; Fatemah Alghamdi; A. A. Abdel-Salam; M. Khalifa Saad; Nural Yüksel; Nurdan Oğraş; Fatemah Alghamdi; A. A. Abdel-Salam

doi:10.3934/math.2024610

AIMS Mathematics

2024, Volume 9, Issue 5: 12479-12493. doi: 10.3934/math.2024610

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Geometry of tubular surfaces and their focal surfaces in Euclidean 3-space

1.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA
2.
Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey
3.
Financial Sciences Department, Applied College, Imam Abdulrahman Bin Faisal University, KSA
4.
Department of Mathematics, Applied College, Northern Border University, Rafha, KSA

Received: 29 January 2024 Revised: 21 March 2024 Accepted: 25 March 2024 Published: 01 April 2024
MSC : 53A05, 53B25

In this study, we examined the focal surfaces of tubular surfaces in Euclidean 3-space $ E^{3} $. We achieved some significant results for these surfaces in accordance with the modified orthogonal frame. Additionally, we proposed a few geometric invariants that illustrated the geometric characteristics of these surfaces, such as flat, minimal, Weingarten, and linear-Weingarten surfaces, using the traditional methods of differential geometry. Additionally, the asymptotic and geodesic curves of these surfaces have been researched. At last, we presented an example as an instance of use to validate our theoretical findings.
- tubular surfaces,
- focal surfaces,
- modified orthogonal frame
Citation: M. Khalifa Saad, Nural Yüksel, Nurdan Oğraş, Fatemah Alghamdi, A. A. Abdel-Salam. Geometry of tubular surfaces and their focal surfaces in Euclidean 3-space[J]. AIMS Mathematics, 2024, 9(5): 12479-12493. doi: 10.3934/math.2024610

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Abstract

In this study, we examined the focal surfaces of tubular surfaces in Euclidean 3-space $ E^{3} $. We achieved some significant results for these surfaces in accordance with the modified orthogonal frame. Additionally, we proposed a few geometric invariants that illustrated the geometric characteristics of these surfaces, such as flat, minimal, Weingarten, and linear-Weingarten surfaces, using the traditional methods of differential geometry. Additionally, the asymptotic and geodesic curves of these surfaces have been researched. At last, we presented an example as an instance of use to validate our theoretical findings.

References

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