An anomaly formula for Ray–Singer metrics on manifolds with boundary
[Formules d'anomalie pour les métriques de Ray–Singer sur les variétés à bord]
Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 603-608.

On annonce une formule d'anomalie pour les métriques de Ray–Singer d'un fibré plat F sur une variété à bord X . On ne suppose ni que la métrique sur F est plate, ni que la métrique sur X a une structure produit près du bord.

We establish an anomaly formula for Ray–Singer metrics defined by a Hermitian metric on a flat vector bundle over a Riemannian manifold with boundary. We do not assume that the Hermitian metric on the flat vector bundle is flat, nor that the Riemannian metric has product structure near the boundary.

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DOI : 10.1016/S1631-073X(02)02496-2
Brüning, Jochen 1 ; Ma, Xiaonan 2

1 Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin, Germany
2 Centre de mathématiques, École polytechnique, 91128 Palaiseau cedex, France
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Brüning, Jochen; Ma, Xiaonan. An anomaly formula for Ray–Singer metrics on manifolds with boundary. Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 603-608. doi : 10.1016/S1631-073X(02)02496-2. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02496-2/

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