We prove that the reduced holonomy group of a complete smooth solution to the Ricci flow of uniformly bounded curvature cannot spontaneously contract within the lifetime of the solution. It follows then, from an earlier result of Hamilton, that the holonomy is exactly preserved by the equation. In particular, a solution to the Ricci flow may be Kähler or locally reducible at t = T if and only if the same is true of g(t) at times t ≤ T .
ASJC Scopus subject areas
- Applied Mathematics