An anomaly formula for Ray–Singer metrics on manifolds with boundary |
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Authors: | J. Brüning Xiaonan Ma |
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Affiliation: | 1. Institut für Mathematik der Humboldt-Universit?t zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany 2. UMR 7640 du CNRS, Centre de Mathématiques, école Polytechnique, 91128, Palaiseau Cedex, France
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Abstract: | Using the heat kernel, we derive first a local Gauss–Bonnet–Chern theorem for manifolds with a non-product metric near the boundary. Then 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, not assuming that the Hermitian metric on the flat vector bundle is flat nor that the Riemannian metric has product structure near the boundary. Received: January 2004; Revision: February 2005; Accepted: September 2005 |
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Keywords: | Ray– Singer analytic torsion anomaly formula characteristic classes |
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