Curvature identities for Einstein manifolds of dimension 5 and 6

2022/01/31 by Yunhee Euh, Jihun Kim, Euh, Yunhee +3
Computer Science · Mathematics · Physics and Astronomy · #53B20 #53C25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2201.13014

openalex publication_date 2022/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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