Inhalt des Dokuments
Preprint 546-1997
Hypersurfaces with Locally Symmetric Conormal Connection
Author(s) :
Martin Wiehe
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 546-1997
MSC 2000
- 53A15 Affine differential geometry
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53B05 Linear and affine connections
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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