To overcome the limitations of existing spiking graph neural networks (SNNs) confined to Euclidean space, this paper proposes a novel spiking GNN, \method{} , that takes curvature into account. \method{} consists of a Riemannian embedding layer that projects node features onto a manifold with constant curvature, a manifold spiking layer that models membrane potential evolution and spiking behavior in the curved space using curvature-based attention, and a manifold learning objective function that enables instance-specific geometric adaptation via classification and link prediction losses defined on geodesic distances. It is trained using Riemannian SGD, and various benchmark experiments demonstrate that it achieves better accuracy, robustness, and energy efficiency than existing Euclidean SNNs and manifold-based GNNs.
