Korean J. Math. Vol. 25 No. 4 (2017) pp.537-554
DOI: https://doi.org/10.11568/kjm.2017.25.4.537

Surfaces foliated by ellipses with constant Gaussian curvature in Euclidean 3-space

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Published: Dec 30, 2017
Keywords:
Surfaces in Euclidean space, Gaussian curvature.
Mathematics Subject Classification:
53A05, 53A17.

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Ahmed T. Ali
Department of Mathematics Faculty of Science King Abdul Aziz University Jeddah 21589, Saudi Arabia.
Fathi Mohamed Hamdoon
Mathematics Department, Faculty of Science Al-Azhar University Assiut branch 71524 Assiut, Egypt.

Abstract

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space E3. We prove the following results: \textbf{(1)} The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K=0. \textbf{(2)} The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.



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References

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