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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 176
On Conformally flat hypersurfaces, Curved flats and Cyclic systems U. Hertrich Jeromin
It will be shown that suitable ``Gauss maps`` associated to a conformally flat hypersurface in $S^{n+1}$ ($ngeq3$) yield normal congruences of circles having a whole one parameter family of conformally flat orthogonal hypersurfaces. However such a ``cyclic system`` is not uniquely associated to a conformally flat hypersurface. The key idea is to show that these Gauss maps are ``curved flats`` in a pseudo Riemannian symmetric space. Additionally in this context some characterizations of three dimensional conformally flat hypersurfaces arise with a new flavour. Moreover, the curved flat approach allows us to handle conformally flat hypersurfaces in the context of integrable system
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