Legal Case Retrieval (LCR) plays a significant role in ensuring judicial justice in various legal systems and has recently received increasing attention in Information Retrieval (IR) research. Existing LCR methods typically encode documents into low-dimensional vectors by using either bag of keywords or pretrained language models. However, such approaches generally overlook the interactions among numerous cases and the hierarchy skeleton between event and event type. In this paper, we propose to construct an event-aware knowledge hypergraph for representing legal cases. And we put forward a SKeleton-aware hYPERgraph representation framework named SKYPER, to learn the case embeddings. Concretely, a global skeleton aggregates coarse-grained type information and roughly locates a case. A local skeleton learns the fine-grained information and precisely locates a case. And SKYPER also uses hyperbolic space strengthens the hierarchy between event and event type and avoids vocabulary mismatch. At the retrieval stage, the SKYPER learned case embedding is leveraged for further case similarity matching with a few annotated similarity ranking data. Extensive experiments demonstrate that SKYPER outperforms existing models on the public LCR datasets LeCard and COLIEE20-T1 in both supervised and unsupervised settings. Especially, the retrieval efficiency is improved by a large margin.