TAILIEUCHUNG - On non-existence of lightlike hypersurfaces of indefinite Kenmotsu space form

In this paper, lightlike hypersurfaces of indefinite Kenmotsu space form are studied. Some characterizations of non-existence of lightlike hypersurfaces of indefinite Kenmotsu space form are given. | Turk J Math 32 (2008) , 127 – 139. ¨ ITAK ˙ c TUB On Non-Existence of Lightlike Hypersurfaces of Indefinite Kenmotsu Space Form Nesip Aktan Abstract In this paper, lightlike hypersurfaces of indefinite Kenmotsu space form are studied. Some characterizations of non-existence of lightlike hypersurfaces of indefinite Kenmotsu space form are given. Key Words: Lightlike hypersurface, Kenmotsu space form 1. Introduction It is well known that in a semi-Riemannian manifold there are three causal types of submanifolds: spacelike, timelike and lightlike, depending on the character of the induced metric on the tangent space. In the third case, due to the degeneracy of the metric, basic differences occur between the study of lightlike submanifolds and classical theory of Riemannian and semi-Riemannian submanifolds (see [8] and [13]). Let M be a lightlike hypersurfaces of a semi-Riemannian manifold. The primary difference in studying the differential geometry of M consists in that the orthogonal vector bundle T M ⊥ to the tangent bundle T M becomes a distribution of rank 1 on M (see [8], page 81). There exist few papers dealing with lightlike hypersurfaces(see [1], [8], [9], [11], [14]). Duggal and Bejancu, discussed the Cauchy Riemann Lightlike submanifolds of an indefinite Kaehler manifold in ([8], chapter 6) and concluded that there exist no totally umbilical lightlike real hypersurfaces of indefinite complex space forms M (c) with c = 0. Kang et al. study a lightlike hypersurface when the ambient manifold is an indefinite 2000 AMS Mathematics Subject Classification: 53C15, 53C25, 53C40, 53C50 127 AKTAN Sasakian manifold and prove that there exist no totally umbilical lightlike hypersurfaces of indefinite Sasakian space forms M(c) with c = 1 particularly in [11]. G¨ une¸s et al. study a lightlike hypersurfaces of a semi-Riemannain manifold and they show that a lightlike hypersurface is totally geodesic if and only if it is locally symmetric in [9]. S¸ahin and G¨ une¸s .

• Toán học
• Lightlike hypersurface
• Kenmotsu space form
• Non existence
• Indefinite Kenmotsu space
• Semi Riemannian manifold
• Pseudosymmetric lightlike hypersurfaces
• Semisymmetric lightlike hypersurface
• Ricci semisymmetric lightlike hypersurface
• Pseudosymmetric lightlike hypersurface
• Pseudosymmetry condition
• Degenerate metric
• Screen conformal lightlike hypersurface
• Parallel lightlike hypersurface
• Semi symmetric lightlike hypersurface
• Minkowski spacetime
• Admissible screen distribution
• Pseudo Jacobi operator
• Osserman condition
• Indefinite S manifold