On Integrability of Differential Equations on Manifolds

Abstract

Abstract

In this study we consider the geometrical differential concepts that are needed to formulate the

differential equations on manifolds. The solutions of differential equations are submanifolds of ambient

manifolds. The existence of solutions is provided by Frobenius theorem, where Lie algebras are utilized in

the formulation. Other topics are also considered such as control problems and Mechanical systems.