This paper presents a study of a model of electrons moving in a parent band with uniform Berry curvature. The research shows that strong repulsive interactions can lead to the formation of an anomalous Hall crystal (AHC), a topological state with spontaneously broken continuous translation symmetry. The findings are based on a mapping to a problem of Wigner crystallization in a regular 2D electron gas. The study also reveals that a periodic electrostatic potential can induce a competing state with opposite Chern number. The theory provides a unified perspective for understanding the recently observed integer and fractional quantum anomalous Hall effects in rhombohedral multilayer graphene. The paper also discusses the quantum geometric properties of the parent band and the resulting topological states. The results show that the Chern number of the AHC is equal to the parent Berry curvature, while the Chern number of the Chern insulator is the negative of the parent Berry curvature. The study also demonstrates that the quantum geometric properties of the parent band are crucial for the realization of fractionalized phases. The paper concludes that the results provide a powerful guiding perspective for understanding real systems and that the model can be useful for future studies into the role of Berry curvature in many-body physics.This paper presents a study of a model of electrons moving in a parent band with uniform Berry curvature. The research shows that strong repulsive interactions can lead to the formation of an anomalous Hall crystal (AHC), a topological state with spontaneously broken continuous translation symmetry. The findings are based on a mapping to a problem of Wigner crystallization in a regular 2D electron gas. The study also reveals that a periodic electrostatic potential can induce a competing state with opposite Chern number. The theory provides a unified perspective for understanding the recently observed integer and fractional quantum anomalous Hall effects in rhombohedral multilayer graphene. The paper also discusses the quantum geometric properties of the parent band and the resulting topological states. The results show that the Chern number of the AHC is equal to the parent Berry curvature, while the Chern number of the Chern insulator is the negative of the parent Berry curvature. The study also demonstrates that the quantum geometric properties of the parent band are crucial for the realization of fractionalized phases. The paper concludes that the results provide a powerful guiding perspective for understanding real systems and that the model can be useful for future studies into the role of Berry curvature in many-body physics.