  For a domain \Omega in \mathbb{C} and an operator T in \mathcal{B}_n(\Omega),
Cowen and Douglas construct a Hermitian holomorphic vector bundle E_T over
\Omega corresponding to T. The Hermitian holomorphic vector bundle E_T is
obtained as a pull-back of the tautological bundle S(n,\mathcal{H}) defined
over \mathcal{G}r(n,\mathcal{H}) by a nondegenerate holomorphic map z\mapsto
{\rm{ker}}(T-z) for z\in\Omega. To find the answer to the converse, Cowen and
Douglas studied the jet bundle in their foundational paper. The computations in
this paper for the curvature of the jet bundle are somewhat difficult to
comprehend. They have given a set of invariants to determine if two rank n
Hermitian holomorphic vector bundle are equivalent. These invariants are
complicated and not easy to compute. It is natural to expect that the
equivalence of Hermitian holomorphic jet bundles should be easier to
characterize. In fact, in the case of the Hermitian holomorphic jet bundle
\mathcal{J}_k(\mathcal{L}_f), we have shown that the curvature of the line
bundle \mathcal{L}_f completely determines the class of
\mathcal{J}_k(\mathcal{L}_f). In case of rank n Hermitian Holomorphic vector
bundle E_f, We have calculated the curvature of jet bundle \mathcal{J}_k(E_f)
and also have generalized the trace formula for jet bundle \mathcal{J}_k(E_f).
