  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.
