The generalized Gauss–Bonnet–Chern theorem
The generalized Gauss–Bonnet–Chern theorem
复制标题
广义高斯-邦内-陈省理
DOI：
10.1063/1.531015
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发表时间：
1995
影响因子：
1.3
通讯作者：
L. Alty
中科院分区：
文献类型：
--
作者：
L. Alty
对于有边界的黎曼流形，著名的高斯-博内-陈省身定理给出了流形的欧拉特征线的积分公式。在这里，我们推广了Avez的证明，证明了对于具有任意签名的伪黎曼度量的边界的流形也有类似的结果。在度规是洛伦兹的情况下，广义相对论有一些应用。广义高斯-邦尼-陈省身定理也提供了引力扭折的公式。
For Riemannian manifolds with boundary, the well‐known Gauss–Bonnet–Chern theorem gives an integral formula for the Euler characteristic of the manifold. Here we extend a proof by Avez to show that there is a similar result for manifolds with boundary endowed with a pseudo–Riemannian metric of arbitrary signature. In the case when the metric is Lorentzian there are some applications to general relativity. The generalized Gauss–Bonnet–Chern theorem also provides a formula for the gravitational kink.