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A symmetric space is a connected Riemannian manifold in which at every point there exists a global self-isometry whose differential at the given point is minus identity.

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Closed manifolds of nonnegative curvature operator are symmetric spaces

As Igor Belegradek commented, the correct statement is as follows: Theorem (classification of closed simply connected manifold with nonnegative curvature operator): A closed simply connected manifold …
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Closed manifolds of nonnegative curvature operator are symmetric spaces

In an online webinar, I heard (not directly) the statement that (closed) manifolds of nonnegative curvature operator $\mathcal{R}\geq 0$ are symmetric spaces. Is this a valid theorem? Any reference t …
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