We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. | Turk J Math 34 (2010) , 561 – 583. ¨ ITAK ˙ c TUB doi: Transversal lightlike submanifolds of indefinite sasakian manifolds Cumali Yıldırım and Bayram S ¸ ahin Abstract We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical transversal lightlike submanifolds. Key Words: Indefinite Sasakian Manifold, Lightlike Submanifold, Radical Transversal Lightlike Submanifold, Transversal Lightlike Submanifold. 1. Introduction ¯ is called lightlike (degenerate) submanifold if the A submanifold M of a semi-Riemannian manifold M induced metric on M is degenerate. Lightlike submanifolds have been studied widely in mathematical physics. Indeed, lightlike submanifolds appear in general relativity as some smooth parts of event horizons of the Kruskal and Kerr black holes [10]. Lightlike submanifolds of semi-Riemannian manifold have been studied by DuggalBejancu and Kupeli in [4] and [12], respectively. Kupeli’s approach is intrinsic while Duggal-Bejancu’s approach is extrinsic. Lightlike submanifolds of indefinite Sasakian manifolds are defined according to the behaviour of the almost contact structure of indefinite Sasakian manifolds and such submanifolds were studied by in [8]. They defined and studied invariant, screen real, contact CR-lightlike and screen CR-lightlike submanifolds of indefinite Sasakian manifolds. Later on, Duggal and studied contact generalized CRlightlike submanifolds of indefinite Sasakian manifolds [9]. It is known that contact geometry has been used differential equations, optics, and phase spaces of a .
