Evolution of an extended Ricci flow system

摘要

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.