Ma, Xiaonan Analytic torsion forms and families of submersions. (Formes de torsion analytique et familles de submersions.) (French. Abridged English version) Zbl 0880.32015 C. R. Acad. Sci., Paris, Sér. I 324, No. 2, 205-210 (1997). 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. Reviewer: A.V.Chernecky (Odessa) Cited in 1 ReviewCited in 4 Documents 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 Keywords:holomorphic fiber spaces; Hermitian metric on vector bundle; topology of vector bundles and fiber bundles Citations:Zbl 0804.32017 PDFBibTeX XMLCite \textit{X. Ma}, C. R. Acad. Sci., Paris, Sér. I 324, No. 2, 205--210 (1997; Zbl 0880.32015) Full Text: DOI