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arXiv · 2006.01611

Sectionally positive curvature tensors admit a metric tensor under which they are Einstein

Dan Gregorian Fodor
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Abstract

Let $n \geq 3$ and $R_{abcd}$ be a $(4,0)$ sectionally positive curvature-type tensor (a tensor possessing all the local symmetries of the $(4,0)$ curvature tensor). Then there exists a metric tensor $g_{ab}$ such that $R_{abcd}\; g^{bd} = g_{ac} \lambda$ for some $\lambda$. Furthermore, $g_{ab}$ is unique up to a constant factor.

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Dan Gregorian Fodor. 2020-06-02. Sectionally positive curvature tensors admit a metric tensor under which they are Einstein. https://arxiv.org/abs/2006.01611

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