Parkinson's disease (PD) is characterized by motor alterations and associated with dopamine neurotransmitters degeneration, affecting 3 % of the population over 65 years of age. Today, there is no definitive biomarker for an early diagnosis and progression characterization. Recently, oculomotor alterations have shown promising evidence to quantify PD patterns. Current capture and oculomotor setups however require sophisticated protocols, limiting the analysis to coarse measures that poorly exploit alterations and restrict their standard use in clinical environments. Computational based deep learning strategies today bring a robust alternative by discovering in video sequences hidden patterns associated to the disease. However, these approaches are dependent on large training data volumes to cover the variability of patterns of interest. This work introduces a novel strategy that exploits data geometry within a deep Riemannian manifold, withstanding data scarcity and discovering oculomotor PD hidden patterns. First, oculomotor information is encoded as symmetric matrices that capture second order statistics of deep features computed by a convolutional scheme. These symmetric matrices then form an embedded representation, which is decoded by a Riemannian network to discriminate Parkinsonian patients w.r.t a control population. The proposed strategy, evaluated on a fixational eye experiment, proves to be a promising approach to represent PD patterns.