Abstract. We study the geometry of lightlike submanifolds of a semi-Riemannian manifold. The purpose of this paper is to prove two singulartheorems for irrotational lightlike submanifolds M of a semi-Riemannianspace form M(c) admitting a semi-symmetric non-metric connection suchthat the structure vector eld of M(c) is tangent to M. 1. IntroductionThe theory of lightlike submanifolds is an important topic of research indi erential geometry due to its application in mathematical physics, especiallyin the general relativity. The study of such notion was initiated by Duggal andBejancu [3] and later studied by many authors (see up-to date results in twobooks [4, 7]). Recently many authors have studied lightlike submanifolds Mof inde nite almost contact metric manifolds M (see [5, 6, 7, 8, 14, 16]). Theauthors in above papers principally assumed that the structure vector eld of M is tangent to M. Calin proved the following result in his thesis:Calin’s result [2]: If the structure vector eld of M is tangent to M, thenit belongs to the screen distribution S(TM) of M.After Calin’s work, many earlier works [5, 6, 7, 14, 16], which have been writ-ten on lightlike submanifolds of inde nite almost contact metric manifolds,obtained their results by using the Calin’s result described in above.The notion of a semi-symmetric non-metric connection on a Riemannianmanifold was introduced by Ageshe and Chae [1]. Although now we havelightlike version of a large variety of Riemannian submanifolds, the geometry oflightlike submanifolds of semi-Riemannian manifolds admitting semi-symmetricnon-metric connections has been few known. Several works ([9]˘[13]), whichhave been written on lightlike submanifolds of semi-Riemannian manifolds ad-mitting semi-symmetric non-metric connections, also obtained their results by