A Report on Canonical Null Curves and Screen Distributions for Lightlike Geometry

• Autores: K. L. Duggal
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 95, Nº. 2, 2007, págs. 135-149
• Idioma: inglés
• DOI: 10.1007/s10440-006-9082-x
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• Resumen

  • The general theory of lightlike 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 purpose 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. We also prove a new theorem on the existence of an integrable canonical screen, subject to a geometric condition, and supported by a physical application.