quantum mechanics - Berry curvature in one dimensional parameter space

Berry curvature is defined by

$$\Omega_{n,\mu\nu}(R) = \frac{\partial A_{n,\nu}}{\partial R^{\mu}} - \frac{\partial A_{n,\mu}}{\partial R^{\nu}} $$ where $R$ is an parameter in hamiltonian. I think it is well defined if the dimension of parameter $R$ is more than 2. But what if the dimension of parameter $R$ is 1? Is it possible to say something about Berry curvature if the dimension of parameter is 1? If the dimension is 1, I think even the closed path integral for Berry phase is not well derfined.