  The perturbative double copy is by now a highly established correspondence
between gravity and gauge theories. Non-perturbatively, information ranging
from classical solutions to topological quantities on both sides have been
related to each other via the double copy correspondence. In this paper, we add
another result, where we show that the single copy of the Ricci flow is the
Yang-Mills flow on the space of connections of a principal
$\text{U}(1)$-bundle.
