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Sectional Curvature Pinching of Two-Step Nilmanifolds
We study the classical problem of sectional curvature pinching in the class of 2-step nilmanifolds, which are necessarily of mixed curvature. We show that the pinching constant of any 2-step nilmanifold lies in the compact interval $[-3, -\frac{3}{2}]$. The upper bound $-\frac{3}{2}$ is achieved by
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