DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES
Abstract
We show that on a non-minimal lightlike hypersurface with nullity
degree 1, there exists a unique null transversal (normalizing) vector eld with
prescribed calibrated divergence, for which the induced connection and the LeviCivita
connection of the associate non-degenerate metric coincide.
Keywords
Lightlike hypersurface, normalization, associate metric, invariant normalizing di erential equation
References
- Akivis, M. A. and Goldberg, V. V. On Some Methods of Construction of Invariant Normaliza- tions of Lightlike Hypersurfaces. Di . Geom. Appl. 12 (2000), p. 121-143.
- Akivis, M. A. and Goldberg, V. V. Lightlike Hypersurfaces on Manifolds Endowed with a Con- formal Structur of Lorentzian Signature. Acta Appl. Math. 57 (1999), p.155-185.
- Atindogbe, C.Normalization and prescribed extrinsic scalar curvature on lightlike hypersurfaces, Journal of Geometry and Physics 60 (2010) 1762â1770.
- Atindogbe, C. Blaschke type normalization on light-Like Hypersurfaces, Journal of Mathemat- ical Physics, Analysis, Geometry 6 (2010) No. 4, pp. 362-382.
- Atindogbe, C. Scalar curvature on lightlike hypersurfaces Applied Sciences, Vol.11, 2009, pp. 18.
- Atindogbe, C. and Ezin, J.-P. and J. Tossa Pseudo-inversion of degenerate metrics Int. J. of Mathematics and Mathematical Sciences, 55 (2003), 3479-3501.
- Atindogbe, C. and K.L. Duggal, K. L. Conformal screen on lightlike hypersurfaces., Int. J. of Pure and Applied Math., 11 (2004), 421-442.
- E. Bekkara, C. Frances and A. Zeghib On lightlike geometry: isometric actions and rigidity aspects. C. R. Acad. Sci. Paris, Ser. (2006), 1343, p. 317-321.
- Carter, B. Killing Horizons and Orthogonally Transitive Groups in Space-time. J. Math. Phys. (1969), 1, p. 70-81.
- Chrusciel, P. T. Delay, E. and Galloway, G. J. Howard, R. Regularity of the horizon and the Area Theorem, Annales Henri Poincaré, 2001,2, p.109-178. gr-qc/0001003.