The BFK-gluing formula and the curvature tensors on a 2-dimensional compact hypersurface

Understand

In the proof of the BFK-gluing formula for zeta-determinants of Laplacians there appears a real polynomial whose constant term is an important ingredient in the gluing formula.

• This polynomial is determined by geometric data on an arbitrarily small collar neighborhood of a cutting hypersurface.
• In this paper we express the coefficients of this polynomial in terms of the scalar and principal curvatures of the cutting hypersurface embedded in the manifold when this hypersurface is 2-dimensional.
• Similarly, we express some coefficients of the heat trace asymptotics of the Dirichlet-to-Neumann operator in terms of the scalar and principal curvatures of the cutting hypersurface.