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

In this paper, we study the surfaces foliated by  ellipses in three dimensional Euclidean space E³. We prove the following results: (1) The surface  foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. $K=0$. (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.