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Self-supervised learning (especially contrastive learning) methods on heterogeneous graphs can effectively get rid of the dependence on supervisory data. Meanwhile, most existing representation learning methods embed the heterogeneous graphs into a single geometric space, either Euclidean or hyperbolic. This kind of single geometric view is usually not enough to observe the complete picture of heterogeneous graphs due to their rich semantics and complex structures. Under these observations, this paper proposes a novel self-supervised learning method, termed as Geometry Contrastive Learning (GCL), to better represent the heterogeneous graphs when supervisory data is unavailable. GCL views a heterogeneous graph from Euclidean and hyperbolic perspective simultaneously, aiming to make a strong merger of the ability of modeling rich semantics and complex structures, which is expected to bring in more benefits for downstream tasks. GCL maximizes the mutual information between two geometric views by contrasting representations at both local-local and local-global semantic levels. Extensive experiments on four benchmarks data sets show that the proposed approach outperforms the strong baselines, including both unsupervised methods and supervised methods, on three tasks, including node classification, node clustering and similarity search.