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Abstract:
We show that Hamilton's Ricci flow and the static Einstein vacuum equations are closely connected by the following system of geometric evolution equations:
partial derivative(t)g = -2Rc(g) + 2 alpha(n)du circle times du, partial derivative(t)u = Delta(g)u, where g(t) is a Riemannian metric, u(t) a scalar function and an a constant depending only on the dimension n >= 3. This provides an interesting and useful link from problems in low-dimensional topology and geometry to physical questions in general relativity.
