Lightlike Hypersurfaces of Semi-Riemannian Manifolds

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


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.


Vector Bundle Fundamental Form Lorentz Space Shape Operator Linear Connection 
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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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