Every connected closed Einstein four-manifold with positive Einstein constant and nonnegative sectional curvature that has even one zero-curvature two-plane has universal Riemannian cover isometric to a product of two equal-radius round two-spheres.
Every connected closed Einstein four-manifold with positive Einstein constant and nonnegative sectional curvature that has even one zero-curvature two-plane has universal Riemannian cover isometric to a product of two equal-radius round two-spheres.
Every connected closed Einstein four-manifold with positive Einstein constant and nonnegative sectional curvature that has even one zero-curvature two-plane has universal Riemannian cover isometric to a product of two equal-radius round two-spheres.
If correct, determines the boundary case of the nonnegative sectional-curvature classification.
Does one zero-curvature plane force product geometry in a nonnegatively curved Einstein four-manifold?
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OpenAI reports zero-plane rigidity for Einstein four-manifolds
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