%0 Journal Article
%T Surfaces with central cross-sections
%A Bruce Solomon
%J Mathematics
%D 2009
%I arXiv
%X A surface S in R^3 has the central plane oval property (cpo) if (i) S meets at least one affine plane transversally along a strictly convex oval, and (ii) Every such transverse oval on S has central symmetry. We show that a complete, connected C^2 surface with cpo must be either a generalized cylinder, or quadric. Applying this, we deduce that a complete C^2 surface containing a transverse plane oval but no skewloop, must be a cylinder or a quadric.
%U http://arxiv.org/abs/0904.3493v2