Evolution of an extended Ricci flow system

List, Bernhard

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Journal Article

Evolution of an extended Ricci flow system

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List, Bernhard
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

List, B. (2008). Evolution of an extended Ricci flow system. Communications in Analysis and Geometry, 16(5), 1007-1048.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-46E6-C

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.