  We define a metric and a family of $\alpha$-connections in statistical
manifolds, based on $\varphi$-divergence, which emerges in the framework of
$\varphi$-families of probability distributions. This metric and
$\alpha$-connections generalize the Fisher information metric and Amari's
$\alpha$-connections. We also investigate the parallel transport associated
with the $\alpha$-connection for $\alpha=1$.
