论文标题
Pfaffian的较高侵犯
Higher transgressions of the Pfaffian
论文作者
论文摘要
我们针对由多层型的单位矢量场的家族定义了任意秩序的侵犯，用于对向量捆绑包的半利曼式指标指标连接的pfaffian。我们将此公式用于计算Riemannian多面体歧管的欧拉（Euler）特征，以Chern的差分几何形式证明，对封闭的歧管和歧管上的歧管上的广义高斯式式公式证明。结果，我们得出了球形和双曲线多面体的身份，该身份连接了偶数偶数的面孔和外角的度量。
We define transgressions of arbitrary order, with respect to families of unit-vector fields indexed by a polytope, for the Pfaffian of metric connections for semi-Riemannian metrics on vector bundles. We apply this formula to compute the Euler characteristic of a Riemannian polyhedral manifold in the spirit of Chern's differential-geometric proof of the generalized Gauss-Bonnet formula on closed manifolds and on manifolds-with-boundary. As a consequence, we derive an identity for spherical and hyperbolic polyhedra linking the volumes of faces of even codimension and the measures of outer angles.
