Let $M$ and $N$ be two complex manifolds of complex dimension $2$.
Let $\mathcal{F}_M,\mathcal{F}_N$ be a singular holomorphic one-dimensional foliation on $M,N$; respectively. Thus, the leaves of the foliations $\mathcal{F}_M,\mathcal{F}_N$ are Riemann surfaces.
Let $L_M,L_N$ be a leaf of the foliation $\mathcal{F}_M,\mathcal{F}_N$; respectively, such that $L_M,L_N$ are diffeomorphic.
Assume that the leaf $L_M$ is a hyperbolic Riemann surface (i.e., the volume of the leaf $L_M$ grows exponentially).
Under the assumptions above, is the leaf $L_N$ a hyperbolic Riemann surface as well?