Degenerate Monge-Type Hypersurfaces
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Abstract
In this note, we extend the notion of a Monge hypersurface from its roots in semi-Euclidean space to more general spaces. For the degenerate case, the geometry of these structures is studied using the Bejancu-Duggal method of screen distributions.
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Pham, D.
(2014).
Degenerate Monge-Type Hypersurfaces.
Acta Mathematica Universitatis Comenianae, 83(1), 67-80.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/78/29
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References
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[15] J. Sultana, C.C. Dyer, Cosmological black holes: A black hole in the Einstein-de Sitter universe, Gen. Rel. Grav., 37(8), (2005), 1349-1370.
[2] A. Bejancu, A canonical screen distribution on a degenerate hypersurface, Scientic Bulletin, Series A, Applied Math. and Physics, 55 (1993), 55-61.
[3] A. Bejancu, A. Ferrandez, and P. Lucas, A new viewpoint on the geometry of a lightlike hypersurface in a semi-Euclidean space, Saitama Math. J. 16, (1998), 31-38.
[4] C. Calin, Totally umbilical degenerate Monge hypersurfaces of $R^4_1$, Publications de L'Institut Mathematique, Novelle serie, tome 60(74), 1996, 137-142.
[5] M.A. Cheshkova, Monge hypersurfaces in Euclidean space, Russian Mathematics, 45(3), (2001), 69-70.
[6] K. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic, 364, 1996.
[7] K. Duggal, A report on canonical null curves and screen distribution for lightlike geometry, Acta. Appl. Math., 95, (2007), 135-149.
[8] K. Duggal, On canonical screen for lightlike submanifolds of codimension two, Central European Journal of Math., 5, (2007), 710-719.
[9] K. Duggal, On existence of canonical screens for coisotropic submanifolds, Int. Electronic J. Geom., 1(1), (2008), 25-32.
[10] K. Duggal, B. Sahin, Dierential Geometry of Lightlike Submanifolds, Birkauser Verlag AG, Bassel 2010.
[11] S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Spacetime, Cambridge University Press, 1973.
[12] D. Kupeli, Singualr Semi-Riemannian Geometry, Kluwer Academic, 366, 1996.
[13] D. Kupeli, On Null Submanifolds in Spacetimes, Geomertiae Dedicata., 23(1), (1987), 33-51.
[14] J. Sultana, C.C. Dyer, Conformal Killing horizons, J. Math. Phys., 45(12), (2004), 4764-4776.
[15] J. Sultana, C.C. Dyer, Cosmological black holes: A black hole in the Einstein-de Sitter universe, Gen. Rel. Grav., 37(8), (2005), 1349-1370.