A classification of Einstein lightlike hypersurfaces of a Lorentzian space form. (English) Zbl 1207.53064
A classical result due to Fialkow and Thomas deals with the classification of connected Einstein hypersurfaces in \(\mathbb R^{n+1}\). The present paper is aimed at providing a light-like version of the above classical result.
Indeed, the authors study light-like hypersurfaces of a distinguished family of semi-Riemannian manifolds of constant curvature. As main result, the authors obtain a classification of Einstein light-like hypersurfaces of Lorentzian space forms.
Indeed, the authors study light-like hypersurfaces of a distinguished family of semi-Riemannian manifolds of constant curvature. As main result, the authors obtain a classification of Einstein light-like hypersurfaces of Lorentzian space forms.
Reviewer: Marco Modugno (Firenze)
MSC:
| 53C40 | Global submanifolds |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
References:
| [1] | Fialkow, A., Hypersurfaces of a space of constant curvature, Ann. of Math., 39, 762-785 (1938) · JFM 64.1361.03 |
| [2] | Thomas, T. Y., On closed spaces of constant mean curvature, Amer. J. Math., 58, 702-704 (1936) · Zbl 0015.27303 |
| [3] | Duggal, K. L.; Jin, D. H., Null Curves and Hypersurfaces of Semi-Riemannian Manifolds (2007), World Scientific · Zbl 1144.53002 |
| [4] | Duggal, K. L., On scalar curvature in lightlike geometry, J. Geom. Phys., 57, 473-481 (2007) · Zbl 1107.53047 |
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| [7] | Duggal, K. L., A report on canonical null curves and screen distributions for lightlike geometry, Acta Appl. Math., 95, 135-149 (2007) · Zbl 1117.53019 |
| [8] | Duggal, K. L.; Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications (1996), Kluwer Acad. Publishers: Kluwer Acad. Publishers Dordrecht · Zbl 0848.53001 |
| [9] | Atindogbe, C.; Ezin, J.-P.; Tossa, J., Lightlike Einstein hypersurfaces in Lorentzian manifolds with constant curvature, Kodai Math. J., 29, 1, 58-71 (2006) · Zbl 1101.53039 |
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