In space-air-ground integrated networks (SAGIN), receivers experience diverse interference from both the satellite and terrestrial transmitters. The heterogeneous structure of SAGIN poses challenges for traditional interference management (IM) schemes to effectively mitigate interference. To address this, a novel UAV-RIS-aided IM scheme is proposed for SAGIN, where different types of channel state information (CSI) including no CSI, instantaneous CSI, and delayed CSI, are considered. According to the types of CSI, interference alignment, beamforming, and space-time precoding are designed at the satellite and terrestrial transmitter side, and meanwhile, the UAV-RIS is introduced for cooperating interference elimination process. Additionally, the degrees of freedom (DoF) obtained by the proposed IM scheme are discussed in depth when the number of antennas on the satellite side is insufficient. Simulation results show that the proposed IM scheme improves the system capacity in different CSI scenarios, and the performance is better than the existing IM benchmarks without UAV-RIS.