In this paper, we consider two maximal monotone vector fields A and B with the corresponding resolvents \(J^A\) and \(J^B\) and their generated semigroups \(S^A\) and \(S^B\) on an Hadamard manifold, and then we prove that the semigroup associated to the maximal monotone vector field \(A+B\) , say \(S^{A+B}\) , is generated by the resolvents \(J^A\) and \(J^B\) as well as by the semigroups \(S^A\) and \(S^B\) . This well-known result on Hilbert spaces is called the Lie–Trotter–Kato theorem. Finally, an application to convex minimization problem is presented.
