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Ricci flow

- A significant 2-dimensional example is the , which is given by the metric ( dx 2 dy 2)/( e 4 t x 2 y 2) on the Euclidean plane. Although this metric shrinks under the Ricci flow, its geometry remains the same. Such solutions are called steady Ricci solitons. An example of a 3-dimensional steady Ricci soliton is the "Bryant soliton", which is rotationally symmetric, has positive curvature, and is obtained by solving a system of ordinary differential equations.

Relationship to uniformization and geometrization

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