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