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Gaussian curvature, mean curvature, sectional curvature, scalar curvature, curvature tensors (Riemann, Ricci, Weyl)

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The differentiability of the distance function on asymptotically flat manifolds

If so, then we can study the ODE obeyed by the mean curvature $H_r$ and the traceless part of the second fundamental form $\hat A$. … If the Ricci curvature falls very quickly, I think it can be shown that $H_r = \frac{1}{r} + O(\frac{1}{r^2})$. …