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Conformal Geometry and Dynamics

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A note on conformal connections on lightlike hypersurfaces

Authors: Cyriaque Atindogbe and Lionel Berard-Bergery
Journal: Conform. Geom. Dyn. 11 (2007), 1-11
MSC (2000): Primary 53C50, 53C05, 53C29
Published electronically: January 10, 2007
MathSciNet review: 2276544
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Cyriaque Atindogbe
Affiliation: Institut De Mathématiques et de Sciences Physiques, 01 BP 613, Porto-Novo, Bénin

Lionel Berard-Bergery
Affiliation: Institut Elie Cartan, Université Henri Poincaré, Nancy I, B.P. 239 54506 Vandœuvre-lès Nancy Cedex, France

Keywords: Lightlike hypersurface, screen distribution, conformal connection, holonomy group.
Received by editor(s): December 1, 2005
Published electronically: January 10, 2007
Additional Notes: The first author thanks the Agence Universitaire de la Francophonie (AUF) for support with a one year research grant, along with the Institut Elie Cartan (IECN, UHP-Nancy I) for research facilities during the completion of this work.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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