Say that a surface in has the central plane oval property, or cpo, if
- meets some affine plane transversally along an oval, and
- Every such transverse plane oval on has central symmetry.
We show that a complete, connected surface with cpo must either be a cylinder over a central oval, or else quadric. We apply this to deduce that a complete surface containing a transverse plane oval but no skewloop must be cylindrical or quadric.
Cite this article
Bruce Solomon, Surfaces with central convex cross-sections. Comment. Math. Helv. 87 (2012), no. 2, pp. 243–270DOI 10.4171/CMH/253