Central figure-8 cross-cuts make surfaces cylindrical (Q1707410)

The author studies in this paper a complete connected \(C^2\)-surface from \(\mathbb{R}^{3}\) in general position, intersecting some plane along a clean figure-8 (a loop with total curvature zero) and such that all compact intersections with planes have central symmetry. Also he proves that \(M\) is a (geometric) cylinder over some central figure-8. Finally, in the third and final part of the paper, the author establishes some interesting facts about centrally symmetric loops in the plane.