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On canonical screen for lightlike submanifolds of codimension two. (English) Zbl 1153.53016

The notion of light-like submanifolds was introduced by A. Bejancu and K. L. Duggal [Lightlike submanifolds of semi-Riemannian manifolds and applications. Math. and its Appl. 364, Dordrecht: Kluwer Academic Publishers (1996; Zbl 0848.53001)]. The study of these submanifolds is closely related to the choice of a screen distribution.
In this paper the author studies light-like submanifolds of codimension two. More precisely, it is proved the existence of integrable canonical screen distributions. At the end of the paper an example is given which justifies the obtained results.

MSC:

53B25 Local submanifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53B50 Applications of local differential geometry to the sciences

Citations:

Zbl 0848.53001
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References:

[1] M.A. Akivis and V.V. Goldberg: “On some methods of construction of invariant normalizations of lightlike hypersurfaces”, Differential Geom. Appl., Vol. 12, (2000), pp. 121-143. http://dx.doi.org/10.1016/S0926-2245(00)00008-5; · Zbl 0965.53022
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