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A report on canonical null curves and screen distributions for lightlike geometry. (English) Zbl 1117.53019
The paper under review is a survey paper which can serve as a reference to researchers in light-like geometry and also can stimulate further research on finding more cases of canonical null curves and screens for light-like geometry. The general theory of light-like submanifolds makes use of a non-degenerate screen distribution which is not unique and, therefore, the induced objects (starting from null curves) depend on the choice of a screen, which creates a problem. The main goal of this paper is to report on the existence of a canonical representation of null curves of Lorentzian manifolds and the choice of a canonical or a good screen for large classes of lightlike hypersurfaces of semi-Riemannian manifolds. The author also proves a new theorem on the existence of an integrable canonical screen, subject to a geometric condition, and supported by a physical application.
MSC:
53B25Local submanifolds
53C50Lorentz manifolds, manifolds with indefinite metrics
53B50Applications of local differential geometry to physics
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