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Research Article | Open Access

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

Kemal Eren1, Soley Ersoy2, Mohammad Nazrul Islam Khan3( )
Picode Software, Education Training Consultancy Research and Development and Trade Ltd. Co., Sakarya-54050, Turkey
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya-54050, Turkey
Department of Computer Engineering, College of Computer, Qassim University, Saudi Arabia
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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.

Keywords

constant-angle ruled surfacesdifferential equationsmodified orthogonal frameWeingarten surfacespartial differential equations
CLC number: 53A04, 53A05

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 8364-8381
DOI: 10.3934/math.2025385

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Cite this article:
Eren K, Ersoy S, Khan MNI. Novel theorems on constant angle ruled surfaces with Sasai's interpretation. AIMS Mathematics, 2025, 10(4): 8364-8381. https://doi.org/10.3934/math.2025385

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Received: 04 March 2025
Revised: 29 March 2025
Accepted: 02 April 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)