  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.
