Chow's theorem - Revision history

Vipul: 2 revisions

2008-05-18T19:34:37Z

2 revisions

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Vipul at 09:23, 2 September 2007

2007-09-02T09:23:09Z

← Older revision		Revision as of 09:23, 2 September 2007
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	Let <math>S^2</math> denote the [[2-sphere]] (upto differential structure) and <math>g</math> any [[Riemannian metric]] on <math>S^2</math>. Then, the [[Ricci flow]] on <math>S^2</math> starting from <math>g</math>, becomes positive in finite time.		Let <math>S^2</math> denote the [[2-sphere]] (upto differential structure) and <math>g</math> any [[Riemannian metric]] on <math>S^2</math>. Then, the [[Ricci flow]] on <math>S^2</math> starting from <math>g</math>, becomes positive in finite time.

	This, along with [[Hamilton's theorem]], gives the [[Ricci flow convergence theorem on compact surfaces]] which states that any [[Ricci flow]] starting from a [[Riemannian metric]] on a compact surface converges, at time <math>\infty</math>, to a [[constant-curvature metric]].		This, along with [[Hamilton's theorem on Ricci flows]], gives the [[Ricci flow convergence theorem on compact surfaces]] which states that any [[Ricci flow]] starting from a [[Riemannian metric]] on a compact surface converges, at time <math>\infty</math>, to a [[constant-curvature metric]].

Vipul at 09:22, 2 September 2007

2007-09-02T09:22:47Z

New page

==Statement==

Let <math>S^2</math> denote the [[2-sphere]] (upto differential structure) and <math>g</math> any [[Riemannian metric]] on <math>S^2</math>. Then, the [[Ricci flow]] on <math>S^2</math> starting from <math>g</math>, becomes positive in finite time.

This, along with [[Hamilton's theorem]], gives the [[Ricci flow convergence theorem on compact surfaces]] which states that any [[Ricci flow]] starting from a [[Riemannian metric]] on a compact surface converges, at time <math>\infty</math>, to a [[constant-curvature metric]].