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Lightlike Hypersurfaces of Semi-Riemannian Manifolds

  • Krishan L. Duggal
  • Aurel Bejancu
Part of the Mathematics and Its Applications book series (MAIA, volume 364)

Abstract

Here we develop a theory on the differential geometry of a lightlike hypersurface M of a proper semi-Riemannian manifold \(\bar M\) For this purpose, we introduce a non-degenerate screen distribution and construct the corresponding lightlike transversal vector bundle tr(TM) of M, consistent with the well-known theory of Riemannian submanifolds. This enables one to define the induced geometrical objects such as linear connection, second fundamental form, shape operator, etc., and to obtain the Gauss-Codazzi equations leading to the Fundamental Theorem of lightlike hyper-surfaces. It is noteworthy that the second fundamental form (and, therefore, the results on totally geodesic and totally umbilical lightlike hypersurfaces) is independent of the choice of a screen distribution.

Keywords

Vector Bundle Fundamental Form Lorentz Space Shape Operator Linear Connection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Krishan L. Duggal
    • 1
  • Aurel Bejancu
    • 2
  1. 1.University of WindsorWindsorCanada
  2. 2.Polytechnic Institute of IaşiIaşiRomania

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