Quillen metric

In mathematics, the Quillen metric is a metric on a determinant line bundle. It was introduced by Quillen (1985) for certain elliptic operators over a Riemann surface, and generalized to higher-dimensional manifolds by Bismut and Freed (1986).

References

• Bismut, Jean-Michel; Freed, Daniel S. (1986), "The analysis of elliptic families. I. Metrics and connections on determinant bundles.", Comm. Math. Phys., 106 (1): 159–176, MR 0853982, doi:10.1007/BF01210930 
• Quillen, D. (1985), "Determinants of Cauchy-Riemann operators over a Riemann surface", Functional Analysis and Its Applications, 19 (1): 31–34, MR 0783704, doi:10.1007/BF01086022