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Zbl 1049.53011
Duggal, K. L.; Jin, D. H.
Totally umbilical lightlike submanifolds. (English)
[J] Kodai Math. J. 26, No. 1, 49-68 (2003). ISSN 0386-5991

In the paper under review the authors study the geometry of totally umbilical light-like submanifolds. First they recall some results for light-like submanifolds and their structure equations. Next they prove several new theorems on such submanifolds in semi-Riemannian manifolds of constant curvature. The authors show that the induced Ricci tensor of any totally umbilical light-like submanifold in a manifold of constant curvature is symmetric if and only if its screen distribution is integrable. \par It is worth noticing that many well-known spacetimes have light-like hypersurfaces with an integrable 2-dimensional screen distribution.
[Marian Hotloś (Wrocław)]

MSC 2000:: *53B25 Local submanifolds
53C40 Submanifolds (differential geometry)
53C50 Lorentz manifolds, manifolds with indefinite metrics

Keywords: degenerate metric; totally umbilical submanifold; light-like submanifold

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