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A note on conformal connections on lightlike hypersurfaces
Author(s):
Cyriaque
Atindogbe;
Lionel
Berard-Bergery
Journal:
Conform. Geom. Dyn.
11
(2007),
1-11.
MSC (2000):
Primary 53C50, 53C05, 53C29
Posted:
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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Additional Information:
Cyriaque
Atindogbe
Affiliation:
Institut De Mathématiques et de Sciences Physiques, 01 BP 613, Porto-Novo, Bénin
Email:
atincyr@imsp-uac.org
Lionel
Berard-Bergery
Affiliation:
Institut Elie Cartan, Université Henri Poincaré, Nancy I, B.P. 239 54506 Vandouvre-lès Nancy Cedex, France
Email:
berard@iecn.u-nancy.fr
DOI:
10.1090/S1088-4173-07-00148-8
PII:
S 1088-4173(07)00148-8
Keywords:
Lightlike hypersurface,
screen distribution,
conformal connection,
holonomy group.
Received by editor(s):
December 1, 2005
Posted:
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.
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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