Submersions and equivariant Quillen metrics
This paper fits in the program, developed by J.-M. Bismut, of calculating Quillen metrics of the line bundle sections arising canonically from geometrically defined isomorphisms of inverse determinant cohomology bundles on compact complex manifolds. Previous examples of such work include: \textit{J.-M. Bismut} and \textit{G. Lebeau} [Publ. Math., Inst. Hautes Etud. Sci. 74, 1-297 (1991; Zbl 0784.32010)] on immersions; \textit{A. Berthomieu} and \textit{J.-M. Bismut} [J. Reine Angew. Math. 457, 85-184 (1994; Zbl 0804.32017)] on submersions; and \textit{J.-M. Bismut} [J. Differ. Geom. 41, 53-157 (1995; Zbl 0826.32024)] on equivariant immersions. The paper under review handles the case of a submersion of compact complex manifolds, equivariant with respect to the holomorphic action of a compact Lie group. The formula for the Quillen metric involves equivariant analytic torsion forms.
scientific article; zbMATH DE number 1528715
scientific article