JournalscmhVol. 87, No. 2pp. 243–270

Surfaces with central convex cross-sections

  • Bruce Solomon

    Indiana University, Bloomington, USA
Surfaces with central convex cross-sections cover

Abstract

Say that a surface in SR3S\subset\mathbb{R}^{3} has the central plane oval property, or cpo, if

  • SS meets some affine plane transversally along an oval, and
  • Every such transverse plane oval on SS has central symmetry.

We show that a complete, connected C2C^{2} surface with cpo must either be a cylinder over a central oval, or else quadric. We apply this to deduce that a complete C2C^{2} 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