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

## 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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