The analysis of elliptic families. I. Metrics and connections on determinant bundles

• DOI: 10.1007/bf01210930
• Publication Date: 2005-02-25T20:58:25Z
• Authors: Jean-Michel Bismut; Daniel S. Freed
• Keywords: Elliptic operator; Parametrix

In this paper, we construct the Quillen metric on the determinant bundle associated with a family of elliptic first order differential operators. We also introduce a unitary connection on λ and calculate its curvature. Our results will be applied to the case of Dirac operators in a forthcoming paper.