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May 13, 2022 at 1:00 comment added Matheus Andrade @WillieWong thanks a lot! That settles it then. The book is indeed working with Ricci-flow in 3 dimensions.
May 12, 2022 at 20:18 comment added Willie Wong If the Riemann curvature looks like $R(\theta\otimes\theta)$, this means that the sectional curvature is non-zero only for one plane, and vanishes for all other orthogonal planes. This means that the the geometry should looks like a two dimensional "curved something" $\times$ a $(n-2)$ dimensional flat something. I assume your book is working with Ricci-flow in 3 dimensions, so the $(n-2)$ dimensional flat something would be one-dimensional.
May 12, 2022 at 20:08 history edited Matheus Andrade CC BY-SA 4.0
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May 7, 2022 at 4:40 history asked Matheus Andrade CC BY-SA 4.0