论文标题
截面为正曲率张量允许他们在爱因斯坦的指标张量
Sectionally positive curvature tensors admit a metric tensor under which they are Einstein
论文作者
论文摘要
令$ n \ geq 3 $和$ r_ {abcd} $为$（4,0）$截面为正弯曲型张量（张张量具有$（4,0）$曲率张量的所有本地对称性）。然后存在度量张量$ g_ {ab} $，以便$ r_ {abcd} \; g^{bd} = g_ {ac}λ$对于某些$λ$。此外，$ g_ {ab} $是唯一的唯一因素。
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 $R_{abcd}\; g^{bd} = g_{ac} λ$ for some $λ$. Furthermore, $g_{ab}$ is unique up to a constant factor.
