Developable Surfaces Foliated by General Ellipses in Euclidean Space R 3

Ahmad T. Ali ()
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Ahmad T. Ali: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2023, vol. 11, issue 14, 1-17

Abstract: In this article, we classify the developable surfaces in three-dimensional Euclidean space R 3 that are foliated by general ellipses. We show that the surface has constant Gaussian curvature (CGC) and is foliated by general ellipses if and only if the surface is developable, i.e., the Gaussian curvature G vanishes everywhere. We characterize all developable surfaces foliated by general ellipses. Some of these surfaces are conical surfaces, and the others are surfaces generated by some special base curves.

Keywords: cyclic surfaces; Gaussian curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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