| In 1999 Alan Weinstein presented a procedure to average a family of submanifolds of a Riemannian manifold. We give an improvement of Weinstein's averaging procedure and further adapt it to the settings of symplectic and contact geometry. More precisely, we develop a construction to average isotropic submanifolds of symplectic manifolds and Legendrian submanifolds of contact manifolds. As one of several applications we show that nearby every isotropic (Legendrian) submanifold which is "almost invariant" under a compact group action we can find one which is really invariant. |
