Submanifold averaging in riemannian and symplecitc geometry
Differential Geometry
2007-05-23 v2 Symplectic Geometry
Abstract
We give a construction to obtain canonically an ``isotropic average'' of given -close isotropic submanifolds of a symplectic manifold. To do so we use an improvement of Weinstein's submanifold averaging theorem (obtained in collaboration with H. Karcher) and apply ``Moser's trick''. We also present an application to Hamiltonian group actions.
Cite
@article{arxiv.math/0208203,
title = {Submanifold averaging in riemannian and symplecitc geometry},
author = {Marco Zambon},
journal= {arXiv preprint arXiv:math/0208203},
year = {2007}
}
Comments
New title (old title: "Averaging of isotropic submanifolds"), paper re-written and expanded. Added: improvement of Weinstein's averaging theorem (Section 2), application to Hamiltonian actions (Section 9). Statement of main theorem improved. Introduction re-written