Central cross-sections make surfaces of revolution quadric

Details Central cross-sections make surfaces of revolution quadric Central cross-sections make surfaces of revolution quadric

2007-12-17

arxiv.org/abs/0712.2796v3

Mathematics

Differential Geometry

7 pages

Scientific paper

We prove here that when all planes transverse and nearly perpendicular to the
axis of a surface of revolution intersect it in loops having central symmetry,
the surface must be quadric. It follows that the quadrics are the only surfaces
of revolution without skewloops. Similar statements hold for hypersurfaces of
revolution in higher dimensions.

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