Abstract
We investigate the conormal geometry of relative affine hypersurfaces whose relative metric (Blaschke metric) degenerates on a codimension 1 submanifold. Such hypersurfaces arise in the investigation of compact hypersurfaces which are not diffeomorphic to the sphere. We give a fundamental theorem in terms of the conormal structure. Finally, we present a new, affinely invariant tensor which is defined at the set where the relative metric is degenerate.
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Kriele, M. The fundamental theorem forC∞ immersed affine hypersurfaces with type changing Blaschke metric. J Geom 66, 123–135 (1999). https://doi.org/10.1007/BF01225676
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DOI: https://doi.org/10.1007/BF01225676