For compact locally symmetric spaces, what are the flats looks like? I assume the sectional curvatures are $\ge 0$ and the manifold is compact and locally symmetric. I want to know for any given point $p$, what does the maximum flat through $p$ looks like? Let's assume the rank is 2. Is it always an embedded torus?
2026-05-14 06:18:01.1778739481
What are flats looks like in compact locally symmetric spaces?
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