Analytic continuation, the Chern–Gauss–Bonnet theorem, and the Euler–Lagrange equations in Lovelock theory for indefinite signature metrics
Analytic continuation, the Chern–Gauss–Bonnet theorem, and the Euler–Lagrange equations in Lovelock theory for indefinite signature metrics
复制标题
不定签名度量的洛夫洛克理论中的解析延拓、Chern-Gauss-Bonnet 定理和 Euler-Lagrange 方程
DOI：
10.1016/j.geomphys.2014.11.006
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发表时间：
2015
影响因子：
1.5
通讯作者：
JeongHyeong Park
中科院分区：
文献类型：
--
作者：
P. Gilkey;JeongHyeong Park
我们利用解析延拓直接从黎曼集合的相应结果导出了不定签名（p, q）中与pfaffan相关的欧拉-拉格朗日方程。我们还利用解析延拓直接从黎曼集合下的相应结果导出了具有边界的伪黎曼流形的chern - gas - bonnet定理。切束上的复度量在我们的分析中起着至关重要的作用，我们在这种情况下得到了某些复度量的Chern-Gauss-Bonnet定理的一个版本。
We use analytic continuation to derive the Euler–Lagrange equations associated to the Pfaffian in indefinite signature (p, q) directly from the corresponding result in the Riemannian setting. We also use analytic continuation to derive the Chern–Gauss–Bonnet theorem for pseudo-Riemannian manifolds with boundary directly from the corresponding result in the Riemannian setting. Complex metrics on the tangent bundle play a crucial role in our analysis and we obtain a version of the Chern–Gauss–Bonnet theorem in this setting for certain complex metrics.