The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds of metallic semi-Riemannian manifolds. | Turk J Math (2018) 42: 3133 – 3148 © TÜBİTAK doi: Turkish Journal of Mathematics Research Article Transversal lightlike submanifolds of metallic semi-Riemannian manifolds Feyza Esra ERDOĞAN∗ Department of Mathematics, Faculty of Science, Ege University, İzmir, Turkey Received: Abstract: • Accepted/Published Online: • Final Version: The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds of metallic semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be a metric connection. We also obtain characterization of transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Finally, we give two examples. Key words: Metallic structure, metallic semi-Riemannian manifold, lightlike submanifolds, transversal lightlike submanifolds, radical transversal submanifolds 1. Introduction Lightlike submanifolds are one of the most interesting topics in differential geometry. It is well known that a submanifold of a Riemannian manifold is always a Riemannian one. Contrary to that case, in semi-Riemannian manifolds the induced metric by the semi-Riemann metric on the ambient manifold is not necessarily nondegenerate. Since the induced metric is degenerate on lightlike submanifolds, the tools that are used to investigate the geometry of submanifolds in the Riemannian case are not favorable in the semi-Riemannian case and so the classical theory cannot be used to define any induced object on a lightlike submanifold. The main difficulties arise from the fact that the intersection of the normal bundle and the tangent bundle of a lightlike submanifold is nonzero. In 1996, Duggal and Bejancu [14] put forward the general theory of lightlike submanifolds of semi-Riemannian .
