Curvature, Swan's Theorem and Similarity Classification of Holomorphic Bundles

Chunlan Jiang  (Hebei Normal University)

10:00 am to 11:00 am, Apr 11th, 2014   Science Building A1510

Abstract:

In 1978, M. I .Cowen and R. G. Douglas gave a successful unitarily classification for Hermitian holomorphic vector bundle by using the curvature function. In the same paper, they also raised the similarity classification problem. Specially, in 2009,R. G. Douglas asked the following question: Can one give conditions involving the curvatures which imply that two quasi-free Hilbert modules of multiplicity one are similar?

In this paper, we introduce a class of Hermitian holomorphic vector bundle called as quasi-homogeneous bundle which contains all of the homogeneous bundles and some weak homogenous bundles and give the completely similarity classification theorem of quasi-homogeneous bundles by using curvature functions and the second fundamental forms.