Surfaces with central cross-sections

Details Surfaces with central cross-sections Surfaces with central cross-sections

2009-04-22

arxiv.org/abs/0904.3493v2

Mathematics

Differential Geometry

35 pages, 3 figures

Scientific paper

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.

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