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

Ahmed T. Ali, Fathi Mohamed Hamdoon

Abstract


In this paper, we study the surfaces foliated by  ellipses in three dimensional Euclidean space $\mathbf{E}^3$. 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.


Keywords


Surfaces in Euclidean space, Gaussian curvature.

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References


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DOI: http://dx.doi.org/10.11568/kjm.2017.25.4.537

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