  In this paper, we consider the global regularity for Monge-Amp\`ere type equations with the Neumann boundary conditions on Riemannian manifolds. It is known that the classical solvability of the Neumann boundary value problem is obtained under some necessary assumptions. Our main result extends the main theorem from the case of Euclidean space $R^n$ in [11] to Riemannian manifolds. 
Monge-Amp\`ere type equations with Neumann boundary conditions on   Riemannian manifolds