Averaging of Legendrian submanifolds of contact manifolds

Abstract

We give a procedure to ``average'' canonically $C^1$-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves a Legendrian submanifold almost invariant, there is an invariant Legendrian submanifold nearby.

Extention of results to non co-orientable contact manifolds (Section 5 added). 7 pages