Ricci flow

In differential geometry, the Ricci flow is a process which deforms the metric of a Riemannian manifold in a manner formally analogous to the diffusion of heat.

Mathematical definition

Given a Riemannian manifold with metric tensor g_{ab}, we can compute the

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Ricci tensor R_{ab}, which collects averages of sectional curvatures into a kind of "trace" of the Riemann curvature tensor. If we consider the metric tensor (and the associated Ricci tensor) to be functions of a variable which is usually called "time" (but which may have nothing to do with any physical time), then the Ricci flow may be defined by the evolution equation

Related Topics:
Ricci tensor - Riemann curvature tensor

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:partial_t g_{ij}=-2 R_{ij}

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