Surfaces with Central Convex Cross-sections
نویسنده
چکیده
Say that a surface in S ⊂ R has the central plane oval property, or cpo, if • S meets some affine plane transversally along an oval, and • Every such transverse plane oval on S has central symmetry. We show that a complete, connected C surface with cpo must either be a cylinder over a central oval, or else quadric. We apply this to deduce that a complete C surface containing a transverse plane oval but no skewloop, must be cylindrical or quadric.
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