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.

中文翻译：

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二维紧致超曲面上的BFK粘合公式和曲率张量

在证明Laplacians的zeta行列式的BFK-粘合公式中，出现了一个实多项式，其常数项是粘合公式中的重要成分。该多项式由切削超表面的任意小的轴环邻域上的几何数据确定。在本文中，当该超曲面为二维时，我们用嵌入在流形中的切削超曲面的标量和主曲率来表示该多项式的系数。类似地，我们根据切削超曲面的标量和主曲率表示Dirichlet-to-Neumann算子的热迹渐近性的一些系数。