Bull. Korean Math. Soc. 54 (2017), No. 2, pp. 429–442 https://doi.org/10.4134/BKMS.b151004 pISSN: 1015-8634 / eISSN: 2234-3016 SCREEN ISOTROPIC LEAVES ON LIGHTLIKE HYPERSURFACES OF A LORENTZIAN MANIFOLD Mehmet G¨ ulbahar Abstract. In the present paper, screen isotropic leaves on lightlike hy- persurfaces of a Lorentzian manifold are introduced and studied which are inspired by the definition of isotropic immersions in the Riemannian context. Some examples of such leaves are mentioned. Furthermore, some relations involving curvature invariants are obtained. 1. Introduction The notion of isotropic immersions in Riemannian geometry was firstly in- troduced by B. O’Neill [28] in 1965 as follows: Let ϕ :(M,g) → (  M,  g) be an isometric immersion between Riemannian manifolds (M,g) and (  M,  g). The immersion ϕ is called λ-isotropic if there exists a real valued function λ such that at any point p ∈ M , the second fundamental form h satisfies (1.1) ‖h(X, X )‖ = λ for all unit vector X ∈ T p M . If the function λ is constant at every point of M , then M is called a (constant) isotropic submanifold. Later, the isotropic immersions between non-degenerate manifolds have been studied by many authors in [1, 7, 8, 9, 14, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31] etc. The main purpose of the present paper is to continue this frame of works for degenerate immersions, especially for lightlike hypersurfaces of a Lorentzian manifold. But there are some difficulties about studying isotropy for these submanifolds. The fundamental problems are that the second fundamental form of a lightlike hypersurface is a null vector and a screen distribution on lightlike submanifolds isn’t canonical. Thus, the notion of isotropy in a lightlike hypersurface can be studied only on any leaf of a screen distribution which must be canonical and integrable. Received December 5, 2015; Revised September 7, 2016. 2010 Mathematics Subject Classification. Primary 53C42, 53C50. Key words and phrases. isotropic immersion, lightlike hypersurface, Lorentzian manifold. c 2017 Korean Mathematical Society 429