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http://dx.doi.org/10.7468/jksmeb.2011.18.4.353

THE AXIOM OF INDEFINITE SURFACES IN SEMI-RIEMANNIAN MANIFOLDS

Lee, Jae-Won (Department of Mathematics, Sogang University)
Jin, Dae-Ho (Department of Mathematics, Dongguk University)

Publication Information

The Pure and Applied Mathematics / v.18, no.4, 2011 , pp. 353-359 More about this Journal

Abstract

In this paper, we characterize a semi-Riemannian manifolds satisfies the axiom of indefinite surfaces. We obtain the following result: If a semi-Riemannian manifold satisfies the axiom of indefinite surfaces, then it is a real space form.

Keywords

lightlike submanifolds; totally umbilical; indefinite ${\ell}$ -surfaces;

Citations & Related Records

Reference

1	Kumar, R., Rani, R. & Nagaich, R.K.: The axiom of spheres in semi-Riemannian geometry with lightlike submanifolds. Kodai Math. J. 32 (2009), 52-58. DOI
2	Leung, D.S. & Nomizu, K.: The axiom of spheres in Riemannian geometry. J. Differential Geometry 5 (1971), 487 - 489. DOI
3	O'Neill, B.: Semi - Riemannian Geometry with Applications to Relativity. Academic Press, 1983.
4	Cartan, E.: Lecons sur la geometrie des espaces de Riemann. Paris, Gauthiers-Villars, 1946.
5	Duggal, K.L. & Bejancu, A.: Lightlike Submanifolds of Semi - Riemannian Manifolds and Applications. Kluwer Acad. Publishers, Dordrecht, 1996.
6	Duggal, K.L. & Jin, D.H.: Totally umbilical lightlike submanifolds. Kodai Math. J. 26 (2003), 49-68. DOI
7	Graves, L. & Nomizu, K.: On sectional curvature of indefinite metric I. Math. Ann. 232 (1978), 267 - 272. DOI ScienceOn