Geometry is one of the central principles in condensed matter physics: it efficiently compresses the information regarding fluctuation and entanglement of complex quantum states and strongly constrains the correlation of many particles. One of the most famous geometric implications in condensed matter physics is the elegant proof of robust quantization of the integer quantum Hall plateau, due to Thouless, Niu, and Wu, which relates Hall conductivity to flux space curvature. In general, geometries are defined for arbitrary parameter spaces, and important geometric quantities also include metrics. This talk focuses on ideal bands, which are quantum systems saturating geometric bounds in flux space. We show that ideal bands precisely realize the lowest Landau levels on curved space. Building upon ideal bands, we systematically construct their higher Landau level partners, termed generalized Landau levels, and demonstrate quantized geometric invariants. Geometrically, ideal bands and generalized Landau levels are holomorphic curves and associated moving frames. Finally, we discuss the Hall viscosity associated with ideal bands and generalized Landau levels, which are response coefficients for area-preserving deformations and represent curvature in the moduli space. We explore the implications for moiré materials and propose moiré systems as an experimentally feasible platform to simulate quantum Hall problems on curved space.