The curvature of a contraction T in the Cowen-Douglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. ...

In this thesis we study some questions related to vector bundles over hypersurfaces. More precisely, for hypersurfaces of dimension ≥ 2, we study the extension problem of vector bundles. We find some cohomological conditions ...