Hulahoop surfaces (Q1207032)

According to the authors, a hulahoop surface is a smooth surface in Euclidean 3-space which is obtained by rotating a circle around a suitable straight line in space. It is shown that compact smooth surfaces of revolution containing at least two circles through each point must either be a sphere or a hulahoop surface. In the latter case there are two possibilities. a) The axis of rotation belongs to the plane of the circle. Hence we have an ordinary torus with exactly four circles through each point. b) We have a more general hulahoop surface with exactly five circles through each point.