Children born preterm are at risk for a wide range of neurocognitive and neurobehavioral disorders. Some of these may stem from early brain abnormalities at the neonatal age. Hence, a precise characterization of neonatal neuroanatomy may help inform treatment strategies. In particular, the ventricles are often enlarged in neurocognitive disorders, due to atrophy of surrounding tissues. Here we present a new pipeline for the detection of morphological and relative pose differences in the ventricles of premature neonates compared to controls. To this end, we use a new hyperbolic Ricci flow based mapping of the ventricular surfaces of each subjects to the Poincaré disk. Resulting surfaces are then registered to a template, and a between group comparison is performed using multivariate tensor-based morphometry. We also statistically compare the relative pose of the ventricles within the brain between the two groups, by performing a Procrustes alignment between each subject's ventricles and an average shape. For both types of analyses, differences were found in the left ventricles between the two groups.