# geometric charaterization of complex interpolation spaces $(H,Y)_\theta$ where $H$ is a Hilbert space?

Let $C$ be the class of Banach spaces $X$ such that there exists $0<\theta<1$, a Hilbert space $H$ and a Banach space $Y$ such that $$X=(H,Y)_\theta$$ (complex interpolation of Calderon).

Does there exist a geometric charaterization of this class of Banach spaces?

I know that a Banach space $X$ in $C$ is uniformly convex.