| The existence of lagrangian submanifolds of almost symplectic manifolds is studied in this paper. For almost symplectic manifolds of dimension 4 or 6, the existence of lagrangian submanifolds is generic, this can be shown using the Cartan-Kähler theory. But for dimension 8, the Cartan-Kähler theory fails. In this case the existence of lagrangian submanifold is non-generic. This paper introduces the concept of special planes that play an important role in finding lagrangian subspaces or submanifolds. The relationship between the existence of special planes and the existence of lagrangian subspaces are studied. Some results on the existence of lagrangian submanifolds are established. The splitting properties of lagrangian submanifolds are studied and an example of an almost symplectic manifold with lagrangian submanifolds is given. |
