Surfaces with central convex cross-sections

  • Bruce Solomon

    Indiana University, Bloomington, USA


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. 243–270

DOI 10.4171/CMH/253