In this paper, we discuss the new challenges and solutions of managing spectrum in 6G wireless communications when unmanned aerial vehicle (UAV) base stations are equipped with and reconfigurable intelligent surface (RIS). UAV-aided communications can help meet the dynamic traffic demand of mobile crowds. However, the extreme quality of service (QoS) requirement in 6G mobile network poses several challenges of low energy-efficient and insufficient link capacity for UAV communications. However, UAV base station cause the coverage overlapping issues in 3D cellular network and face the energy-limited issue. RIS can adjust the phase shift, amplitude, polarization, and frequency of the incident electromagnetic wave to improve spectral efficiency and reduce interference. The other important spectrum management issue in 6G wireless is to design the efficient and effective spectrum sharing mechanism in a co-existing environment with enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLCs) and massive machine-type communications (mMTCs) traffic flows. The state of the art data-driven deployment strategies and learning-based spectrum management techniques for 6G wireless are surveyed in this paper.