Möbius-flat hypersurface in projective space

Details Möbius-flat hypersurface in projective space Möbius-flat hypersurface in projective space

2012-03-11

arxiv.org/abs/1203.2318v1

Mathematics

Differential Geometry

10 pages

Scientific paper

I give a theory of M\"obius-flat hypersurfaces in n-dimensional projective space, analogous to that in conformal geometry. This unifies the classes of hypersurfaces with flat induced conformal structure (n > 3) and a classically studied class of surfaces (n = 3). I extend an example of Akivis-Konnov, and use polynomial conserved quantities to characterise hypersurfaces with flat centro-affine metric among M\"obius-flat hypersurfaces. The theory has an obvious counterpart in Lie sphere geometry.

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