论文标题
Einstein歧管的曲率身份5和6
Curvature identities for Einstein manifolds of dimension 5 and 6
论文作者
论文摘要
帕特森（Patterson）讨论了[14]中riemannian流形的曲率身份，任何6维里曼尼亚歧管的曲率身份都独立于Chern-Gauss-Bonnet定理[8]。在本文中，我们提供了帕特森曲率身份的显式公式，该公式具有5维和6维的爱因斯坦歧管。我们证实，以前工作[8]中爱因斯坦流形的曲率身份与帕特森结果中得出的曲率身份相同。我们还提供支持定理的示例。
Patterson discussed the curvature identities on Riemannian manifolds in [14], and a curvature identity for any 6-dimensional Riemannian manifold was independently derived from the Chern-Gauss-Bonnet Theorem [8]. In this paper, we provide the explicit formulae of Patterson's curvature identity that holds on 5-dimensional and 6-dimensional Einstein manifolds. We confirm that the curvature identities on the Einstein manifold from the previous work [8] are the same as the curvature identities deduced from Patterson's result. We also provide examples that support the theorems.
