tailieunhanh - Coisotropic submanifolds of a semi-Riemannian manifold

In this paper, we study coisotropic submanifolds of a semi-Riemannian manifold. We investigate the integrability condition of the screen distribution and give a necessary and sufficient condition on Ricci tensor of a coisotropic submanifold to be symmetric. | Turk J Math 28 (2004) , 335 – 352. ¨ ITAK ˙ c TUB Coisotropic Submanifolds of a Semi-Riemannian Manifold∗ Erol Kılı¸c, Bayram S ¸ ahin, H. Bayram Karada˘g, Rıfat G¨ une¸s Abstract In this paper, we study coisotropic submanifolds of a semi-Riemannian manifold. We investigate the integrability condition of the screen distribution and give a necessary and sufficient condition on Ricci tensor of a coisotropic submanifold to be symmetric. Finally, we present some new theorems and results about totally umbilical coisotropic submanifolds of a semi-Riemannian manifold. Key words and phrases: Semi-Riemannian manifold, Lightlike submanifolds, Coisotropic submanifolds. 1. Introduction The geometry of lightlike submanifolds of a semi-Riemannian manifold is one of the interesting topics of differential geometry. In [2], Bejancu-Duggal have constructed a transversal vector bundle of a lightlike submanifold. D. N. Kupeli [5], using the canonical projection, has investigated the properties of these submanifolds. On the other hand, Duggal and Jin have studied totally umbilical half-lightlike submanifolds in semiRiemannian manifolds, of codimension 2 [4]. In this paper, we consider coisotropic submanifolds which were proposed as a research problem by Duggal and Jin in [4]. We obtain a necessary and sufficient condition for integrability of the screen distribution. Also, we investigate Ricci tensor of a coisotropic subMathematics Subject Classification (2000): 53C50, 53C15. ˙ on¨ work was supported by In¨ u University. ∗ This 335 ˙ KARADAG, ˘ GUNES ¨ KILIC ¸, S ¸ AHIN, ¸ manifold and give a necessary and sufficient condition on the Ricci tensor of a coisotropic submanifold to be symmetric. Moreover, we prove that the null sectional curvatures of an ambient space and of a coisotropic submanifold are the same for a totally umbilical coisotropic submanifold. 2. Preliminaries Let (M , g) be a real (m+n)-dimensional semi-Riemannian manifold of constant index q such that m, n

• Toán học
• Semi Riemannian manifold
• Lightlike submanifolds
• Coisotropic submanifolds
• Sufficient condition
• Integrability condition