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Units, Constants and Useful Formulas

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Last modified: December 4, 2021 ✓

Ricci Flow ---------- For a Riemannian manifold the RICCI FLOW is a partial differential equation that evolves the metric tensor over 'time'. It is analogous to the diffusion of heat. ∂gμν(t)/∂t = -2Rμν(gμν(t)) The idea is to smooth out irregularities in the metric and make the geometry of the manifold more symmetric. Informally, it can be considered as the process of stretching the metric in directions of negative Ricci curvature, and contracting the metric in directions of positive Ricci curvature thereby increasing or decreasing the distance between points on the manifold. The greater the curvature, the faster the stretching or contracting. Changing the distances also impacts the angle and area. However, in 2 dimensions the Ricci flow is conformal meaning that angles do not change with the flow.