On canonical screen for lightlike submanifolds of codimension two

• Autorzy: K. Duggal
• Języki publikacji: EN

Abstrakty

EN

In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.

Słowa kluczowe

EN

Half lightlike submanifold; coisotropic submanifold; canonical screen distribution; screen conformal fundamental forms

Kategorie tematyczne

• 53C50: Lorentz manifolds, manifolds with indefinite metrics
• 53B25: Local submanifolds
• 53B50: Applications to physics

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 4
• Strony: 710-719

Daty

wydano

2007-12-01

online

2007-12-01

Twórcy

autor

K. Duggal

• University of Windsor

Bibliografia

• [1] M.A. Akivis and V.V. Goldberg: “On some methods of construction of invariant normalizations of lightlike hypersurfaces”, Differential Geom. Appl., Vol. 12, (2000), pp. 121–143. http://dx.doi.org/10.1016/S0926-2245(00)00008-5
• [2] C. Atindogbe and K.L. Duggal: “Conformal screen on lightlike hypersurfaces”, Int. J. Pure Appl. Math., Vol. 11, (2004), pp. 421–442.
• [3] J.K. Beem and P.E. Ehrlich: Global Lorentzian geometry, Monographs and Textbooks in Pure and Applied Math., Vol. 67, Marcel Dekker, New York, 1981.
• [4] K.L. Duggal: “On scalar curvature in lightlike geometry”, J. Geom. Phys., Vol. 57, (2007), pp. 473–481. http://dx.doi.org/10.1016/j.geomphys.2006.04.001
• [5] K.L. Duggal: “A report on canonical null curves and screen distributions for lightlike geometry”, Acta Appl. Math., Vol. 95, (2007), pp. 135–149. http://dx.doi.org/10.1007/s10440-006-9082-x
• [6] K.L. Duggal and A. Bejancu: “Lightlike submanifolds of codimension two”, Math. J. Toyama Univ., Vol. 15, (1992), pp. 59–82.
• [7] K.L. Duggal and A. Bejancu: Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and its Applications, Vol. 364, Kluwer Academic Publishers Group, Dordrecht, 1996.
• [8] K.L. Duggal and D.H. Jin: “Half lightlike submanifolds of codimension 2”, Math. J. Toyama Univ., Vol. 22, (1999), pp. 121–161.
• [9] K.L. Duggal and B. Sahin: “Screen conformal half-lightlike submanifolds”, Int. J. Math. Math. Sci., Vol. 68, (2004), pp. 3737–3753. http://dx.doi.org/10.1155/S0161171204403342
• [10] K.L. Duggal and A. Giménez: “Lightlike hypersurfaces of Lorentzian manifolds with distinguished screen”, J. Geom. Phys., Vol. 55, (2005), pp. 107–122. http://dx.doi.org/10.1016/j.geomphys.2004.12.004
• [11] D.H. Jin: “Geometry of coisotropic submanifolds”, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., Vol. 8, no. 1, (2001), pp. 33–46.
• [12] B. O’Neill: Semi-Riemannian geometry with applications to relativity, Pure and Applied Mathematics, Vol. 103, Academic Press, New York, 1983.

Identyfikatory

DOI

10.2478/s11533-007-0026-0