The central shadowing property and the Lipschitz product structure for partially hyperbolic diffeomorphisms

Let $ M $ be a Riemannian manifold (not necessarily compact) and $ f:M\to M $ be a partially hyperbolic diffeomorphism with the dynamical coherence. In this paper, we investigate the dynamics of the central shadowing property for $ f $ on $ M $. We demonstrate that every partially hyperbolic diffeomorphism with the Lipschitz product structure admits the central shadowing property.