Four-dimensional homogeneous manifolds satisfying some Einstein-like conditions

Garcı́a-Rı́o, Eduardo; Haji‐Badali, Ali; Mariño-Villar, Rodrigo; Abal, María Elena Vázquez

doi:10.2996/kmj/1605063625

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2021

2023

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Cited by 8 publications

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“…Euh, Park, and Sekigawa [6] dervied a curvature identity on any 4-dimensional manifold from the Chern-Gauss-Bonnet theorem. There are many applications of this identity (see [5,7,9]). On the other hand, Deszcz, Hotloś, and Sentürk [4] gave some curvature properties of 4-dimensional semi-Riemannian manifolds as an application of Patterson's curvature identity.…”

Section: Introductionmentioning

confidence: 99%

Curvature identities for Einstein manifolds of dimension 5 and 6

Euh¹,

Kim²,

Park³

2022

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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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