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2010•arXiv (Cornell University)Open access

A generalization of a 4-dimensional Einstein manifold

Yunhee Euh, JeongHyeong Park, Kouei Sekigawa

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Abstract

A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian manifold. In this paper, we shall give a characterization of a weakly Einstein manifold.

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A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian manifold. In this paper, we shall give a characterization of a weakly Einstein manifold.

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Available abstract

A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian manifold. In this paper, we shall give a characterization of a weakly Einstein manifold.

Key concepts: Einstein, Einstein manifold, Generalization, Manifold (fluid mechanics), Pseudo-Riemannian manifold, Mathematics, Riemannian manifold, Ricci curvature

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