On the planar normal sections in dejenere manifolds

This thesis consists of ve chapters. In the rst chapter, we give basic materialssuch as half-lightlike submanifolds, lightlike submanifolds, degenerate subspaces,semi-Riemannian manifolds, Riemannian manifolds, distributions, vector bundleswhich will be useful for other chapters.In the second chapter , We give necessary and sucient condition for subsmanifoldand semi-Riemannian manifolds to have planar normal sections we also givesome characterizations.In the third chapter, we give certain conditions for a lightlike submanifold of R31to have degenerate or non-degenerate planar normal sections. Then we give somecharacterizations and gives examples.Finally, in the fourth chapter, we give necessary and sucient conditions for ahalf-lightlike submanifold of R42 to have degenerate or non-degenerate planar normalsections. We also give some characterizations and gives examples.KEY WORDS: Lightlike submanifold, Half-lightlike submanifold, Degeneratenormal section, Non-degenerate normal section,Degenerate planar normal section,Non-degenerate planar normal section