On the geometry of CR-manifolds.

Abstract

We study two classes of CR-submanifolds in Kählerian and cosymplectic manifolds. More precisely, we compare the geometry of CR-submanifolds of the above two underlying smooth manifolds. We derive expressions relat- ing the sectional curvatures, the necessary and sufficient conditions for the integrability of distributions. Further, we study totally umbilical, totally geodesic and foliation geometry of the CR-submanifolds of both spaces and found many interesting results. We prove that, under some condition, there are classes CR submanifold in cosymplectic space forms which are in the classes extrinsic spheres. Examples are given throughout the thesis.