Novel theorems on constant angle ruled surfaces with Sasai's interpretation

Kemal Eren; Soley Ersoy; Mohammad Nazrul Islam Khan; Kemal Eren; Soley Ersoy; Mohammad Nazrul Islam Khan

doi:10.3934/math.2025385

AIMS Mathematics

2025, Volume 10, Issue 4: 8364-8381. doi: 10.3934/math.2025385

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Research article

Novel theorems on constant angle ruled surfaces with Sasai's interpretation

1.
Picode Software, Education Training Consultancy Research and Development and Trade Ltd. Co., Sakarya-54050, Turkey
2.
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya-54050, Turkey
3.
Department of Computer Engineering, College of Computer, Qassim University, Saudi Arabia

Received: 04 March 2025 Revised: 29 March 2025 Accepted: 02 April 2025 Published: 11 April 2025
MSC : 53A04, 53A05

In the present study, we investigate constant-angle ruled surfaces constructed by the motion of the elements of each of the modified orthogonal frames along a base curve in three-dimensional Euclidean 3-space. These surfaces are studied and classified based on the constant-angle property. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces by using partial differential equations. Also, we give the conditions for these surfaces to be Weingarten surfaces.
- constant-angle ruled surfaces,
- differential equations,
- modified orthogonal frame,
- Weingarten surfaces,
- partial differential equations
Citation: Kemal Eren, Soley Ersoy, Mohammad Nazrul Islam Khan. Novel theorems on constant angle ruled surfaces with Sasai's interpretation[J]. AIMS Mathematics, 2025, 10(4): 8364-8381. doi: 10.3934/math.2025385

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Abstract

In the present study, we investigate constant-angle ruled surfaces constructed by the motion of the elements of each of the modified orthogonal frames along a base curve in three-dimensional Euclidean 3-space. These surfaces are studied and classified based on the constant-angle property. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces by using partial differential equations. Also, we give the conditions for these surfaces to be Weingarten surfaces.

References

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