A note on conformal connections on lightlike hypersurfaces

Atindogbe, Cyriaque; Berard-Bergery, Lionel

doi:10.1090/S1088-4173-07-00148-8

A note on conformal connections on lightlike hypersurfaces
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by Cyriaque Atindogbe and Lionel Berard-Bergery

Conform. Geom. Dyn. 11 (2007), 1-11

DOI: https://doi.org/10.1090/S1088-4173-07-00148-8

Published electronically: January 10, 2007

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Abstract:

Degenerate submanifolds of pseudo-Riemannian manifolds are quite difficult to study because there is no preferred connection when the submanifold is not totally geodesic. For the particular case of degenerate totally umbilical hypersurfaces, we show that there are “Weyl” connections adapted to the induced structure on the hypersurface. We begin the study of these with their holonomy.

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