An anomaly formula for Ray–Singer metrics on manifolds with boundary
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.
Keywords and phrases.Ray–Singer analytic torsion anomaly formula characteristic classes
AMS Mathematics Subject Classification.58J52 58J28 58J35
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