  An $F$-manifold is complex manifold with a multiplication on the holomorphic
tangent bundle with a certain integrability condition. Important examples are
Frobenius manifolds and especially base spaces of universal unfoldings of
isolated hypersurface singularities. This paper reviews the construction of
hermitian metrics on $F$-manifolds from $tt^*$ geometry. It clarifies the logic
between several notions. It also introduces a new {\it canonical} hermitian
metric. Near irreducible points it makes the manifold almost hyperbolic. This
holds for the singularity case and will hopefully lead to applications there.
