A Convergence Theorem for Riemannian Submanifolds

Abstract

Abstract.In this paper we study the convergence of Riemannian submanifolds. In particular, we prove that any sequence of closed submanifolds with bounded normal curvature and volume in a closed Riemannian manifold subconverge to a closed submanifold in the C1 ,Q topology. We also obtain some applications to irreducible homogeneous manifolds and pseudo-holomorphic curves in symplectic manifolds.

Geometrie

“…Even in the case of Riemannian manifolds, this estimate on the injectivity radius of a submanifold is new as far as we know. Much weaker dimension-dependent estimates have been used in [7] and [16]. The existence of some dimension-independent bound in the general case is proved in [10].…”