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Analytic torsion forms and families of submersions. (Formes de torsion analytique et familles de submersions.) (French. Abridged English version) Zbl 0880.32015

The purpose of this note is to extend to a relative situation a result of Berthomieu-Bismut, [A. Berthomieu and J. M. Bismut, J. Reine Angew. Math. 457, 85-184 (1994; Zbl 0804.32017)] on the behaviour of submersions of Quillen metrics. Let \(\pi_1:W\to V\) (resp. \(\pi_2: V\to S\)) be a holomorphic submersion of complex varieties with compact fibre. Let \(\xi\) be a holomorphic vector bundle on \(W.\) The author’s result relates a combination of the analytic torsion forms associated to \(\pi_1, \pi_2\) and \(\pi_2\circ\pi_1\) in terms of Bott-Chern classes.

MSC:

32L05 Holomorphic bundles and generalizations
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
57R20 Characteristic classes and numbers in differential topology

Citations:

Zbl 0804.32017
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