  We study the critical properties of a non-equilibrium statistical model, the
majority-vote model, on heptagonal and dual heptagonal lattices. Such lattices
have the special feature that they only can be embedded in negatively curved
surfaces. We find, by using Monte Carlo simulations and finite-size analysis,
that the critical exponents $1/\nu$, $\beta/\nu$ and $\gamma/\nu$ are different
from those of the majority-vote model on regular lattices with periodic
boundary condition, which belongs to the same universality class as the
equilibrium Ising model. The exponents are also from those of the Ising model
on a hyperbolic lattice. We argue that the disagreement is caused by the
effective dimensionality of the hyperbolic lattices. By comparative studies, we
find that the critical exponents of the majority-vote model on hyperbolic
lattices satisfy the hyperscaling relation
$2\beta/\nu+\gamma/\nu=D_{\mathrm{eff}}$, where $D_{\mathrm{eff}}$ is an
effective dimension of the lattice. We also investigate the effect of boundary
nodes on the ordering process of the model.
