University ``Al. I. Cuza" of Iasi, Faculty of Mathematics, Bd. Carol I, no. 11, 700506 Iasi, Romania
We introduce a torsion free linear connection on a hypersurface in a Sasakian manifold on which we have defined in natural way a $CR$-structure of $CR$-codimension 2. We study the curvature properties of this connection and we give some interesting examples.
AMSclassification. 53C25, 53C15, 53B15.
Keywords. $CR-$structures, almost contact structures, $f$-structure with complemented frames.