Definition
A flow \((g_t)_{t\in [0,1]}\) of Riemannian metrics is called a Ricci flow if
\begin{align*} \partial_tg_t = -2Rc(g_t) \end{align*}where \(Rc\) is some “average” of sectional survatures, viewing curvature of \(\omega^n\) (the volume form) as a Hamiltonian Metric.
Fact: Ricci flow preserves Kahlerness Fact: All volumes of a complex submanifold are determined by \([\omega_0], c_1(M)\).
Ricci flow can be viewed as a “nonlinear heat equation”. The main theorem to know about these is that these are unique