Blaschke type normalization on light-like hypersurfaces
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (2010), pp. 362-382.

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In this paper we construct and study a Blaschke type normalization on the lightlike hypersurface immersions with 1-degenerate second fundamental form. We discuss basic examples and establish fundamental equations for this canonical transversal vector bundle. As an application, we characterize the Ricci flat 1-degenerate Blaschke immersions.
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     author = {Cyriaque Atindogb\'e},
     title = {Blaschke type normalization on light-like hypersurfaces},
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Cyriaque Atindogbé. Blaschke type normalization on light-like hypersurfaces. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (2010), pp. 362-382. http://geodesic.mathdoc.fr/item/JMAG_2010_6_a1/

[1] M. A. Akivis, V. V. Goldberg, “On Some Methods of Construction of Invariant Normalizations of Lightlike Hypersurfaces”, Diff. Geom. Appl., 12 (2000), 121–143 | DOI | MR | Zbl

[2] M. A. Akivis, V. V. Goldberg, “Lightlike Hypersurfaces on Manifolds Endowed with a Conformal Structure of Lorentzian Signature”, Acta Appl. Math., 57 (1999), 155–185 | DOI | MR

[3] C. Atindogbe, J.-P. Ezin, J. Tossa, “Pseudo-Inversion of Degenerate Metrics”, Int. J. Math. and Math. Sci., 55 (2003), 3479–3501 | DOI | MR | Zbl

[4] C. Atindogbe, K. L. Duggal, “Conformal Screen on Lightlike Hypersurfaces”, Int. J. Pure and Appl. Math., 11:4 (2004), 421–442 | MR | Zbl

[5] E. Bekkara, C. Frances, A. Zeghib, “On Lightlike Geometry: Isometric Actions and Rigidity Aspects”, C.R. Acad. Sci. Paris, 343:5 (2006), 317–321 | DOI | MR | Zbl

[6] B. Carter, “Killing Horizons and Orthogonally Transitive Groups in Space-time”, J. Math. Phys., 10 (1969), 70–81 | DOI | MR | Zbl

[7] G. Dautcourt, “Characteristic Hypersurfaces in General Relativity”, J. Math. Phys., 8 (1967), 1492–1501 | DOI | Zbl

[8] G. Dautcourt, “Zur Differentialgeometrie Singularen Riemannschen Raune”, Math. Nachr., 36 (1968), 311–322 | DOI | MR | Zbl

[9] K. L. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996 | MR | Zbl

[10] K. Katsuno, “Null Hypersurfaces in Lorentzian Manifolds”, Math. Proc. Cab. Phil. Soc., 88 (1980), 175–182 | DOI | MR | Zbl

[11] D. N. Kupeli, “Degenerate Submanifolds in Semi-Riemannian Geometry”, Geometry Dedicata, 24 (1987), 337–361 | MR | Zbl

[12] D. N. Kupeli, “On Null Submanifolds in Spacetimes”, Geometry Dedicata, 23 (1987), 33–51 | MR | Zbl

[13] D. N. Kupeli, Singular Semi-Riemannian Geometry, Kluwer Academic Publishers, Dordrecht, 1996 | MR

[14] J. C. Larsen, “Singular Semi-Riemannian Geometry”, J. Geom. Phys., 9:1 (1992), 3–23 | DOI | MR | Zbl

[15] J. C. Larsen, “Submanifold Geometry”, J. Geom. Anal., 4:2 (1994), 189–205 | DOI | MR

[16] R. Penrose, “The Twistor Geometry of Light Rays”, Geometry and Physics. Classical Quantum Gravity, 14:1A (1997), A299–A323 | DOI | MR | Zbl

[17] M. Pinl, “Zur Theorie del Halbisotrope Flachen im $R4$”, J. Geom. Phys., 9:1 (1992), 3–23 | DOI | MR

[18] R. Rosca, “Sur les Hypersurfaces de Défaut 1 Incluses dans une Variété Lorentzienne”, C.R. Acad. Sci. Paris Sér. A-B, 292 (1971), A393–A396 | MR

[19] R. Rosca, “On Null Hypersurfaces of a Lorentziann Manifolds”, Tensor N.S., 23 (1972), 66–74 | MR | Zbl

[20] A. H. Taub, “Singular Hypersurfaces in General Relativity”, Illinois J. Math., 1 (1957), 378–388 | MR