Hypersurfaces with Locally Symmetric Conormal Connection
نویسنده
چکیده
This paper studies hypersurfaces admitting a locally symmetric connection which is induced by the Gauß conormal map in affine geometry. It is known that the rank of the shape operator is of importance to this topic. In dimension two we give new results for an arbitrary shape operator. In the case of a nondegenerate shape operator hypersurfaces with locally symmetric conormal connection can be treated as semiEuclidean hypersurfaces. Moreover, we study whether and in which way a locally symmetric, projectively flat connection can be realized as the conormal connection of a hypersurface.
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