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arXiv · 1105.3722

Ricci flow and the holonomy group

Brett L. Kotschwar
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Abstract

We prove that the restricted holonomy group of a complete smooth solution to the Ricci flow of uniformly bounded curvature cannot spontaneously contract in finite time; it follows, then, from an earlier result of Hamilton that the holonomy group is exactly preserved by the equation. In particular, a solution to the Ricci flow may be K\"{a}hler or locally reducible (as a product) at $t= T$ if and only if the same is true of $g(t)$ at times $t\leq T$.

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Brett L. Kotschwar. 2011-05-18. Ricci flow and the holonomy group. https://arxiv.org/abs/1105.3722

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