A CONVERGENCE THEOREM FOR RIEMANNIAN SUBMANIFOLDS

In this paper we study the convergence of Riemannian submanifolds. In particular, we prove that any sequence of closed submanifolds with bou nded normal curvature and volume in a closed Riemannian manifold subco nverge to a closed submanifold in the C-1,C-alpha topology. We also ob tain some applications to irreducible homogeneous manifolds and pseudo -holomorphic curves in symplectic manifolds.