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.

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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

Differential geometry: Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for...

Riemannian manifold: In Riemannian geometry, a Riemannian manifold (M, g) is a real differentiable manifold M in which each tangent space is equipped with an inner product < , > in a manner which varies smoothly from point to point. This allows one to define of various notions as the length of curves, angles, areas (or ...

Ricci tensor: REDIRECT Ricci curvature...

Ricci flow related Images and Photos (experimental)

Flow	Hustle & Flow	Christina Ricci	Christina Ricci - Sleepy Hollow
Spice Must Flow Apron	Ebb and Flow	Kilauea Lava Flow Sea Entry Big Island Hawaii	Codex Leicester: Water Flow
Hustle and Flow	Hustle And Flow	Lava Flow at Dusk Volcanoes National Park Hawaii Hawaii	Go with the Flow