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Preprint 546-1997

Hypersurfaces with Locally Symmetric Conormal Connection

Source file is available as :   Postscript Document

Author(s) : Martin Wiehe

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 546-1997

MSC 2000

53A15 Affine differential geometry
53B05 Linear and affine connections
53C35 Symmetric spaces

Abstract :
This paper studies hypersurfaces admitting a locally symmetric connection which is induced by the Gau\ss{} 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 non degenerate shape operator hypersurfaces with locally symmetric conormal connection can be treated as semi-Euclidean 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.

Keywords : Projectively flat connections, locally symmetric connections

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