Trace Formulae for Curvature of Jet Bundles over Planar Domains

Keshari, Dinesh Kumar (2014) Trace Formulae for Curvature of Jet Bundles over Planar Domains. In: COMPLEX ANALYSIS AND OPERATOR THEORY, 8 (8). pp. 1723-1740.

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Abstract

For a domain Omega in C and an operator T in 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, H) defined over by Gr(n, H) a nondegenerate holomorphic map z bar right arrow ker(T - z), z is an element of 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 rather intricate. 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 J(k)(L-f), we have shown that the curvature of the line bundle L-f completely determines the class of J(k)(L-f). In case of rank Hermitian holomorphic vector bundle E-f, We have calculated the curvature of jet bundle J(k)(E-f) and also obtained a trace formula for jet bundle J(k)(E-f).

Item Type:	Journal Article
Publication:	COMPLEX ANALYSIS AND OPERATOR THEORY
Publisher:	SPRINGER BASEL AG
Additional Information:	Copyright for this article belongs to the SPRINGER BASEL AG, PICASSOPLATZ 4, BASEL, 4052, SWITZERLAND
Keywords:	Cowen-Douglas class; Curvature; Hermitian holomorphic vector bundle; Jet bundle
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	19 Dec 2014 07:21
Last Modified:	19 Dec 2014 07:21
URI:	http://eprints.iisc.ac.in/id/eprint/50457

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