Totally geodesic subgroups of diffeomorphisms
Differential Geometry
2009-11-07 v1
Abstract
We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant -metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of symplectic diffeomorphisms in the K\"ahler case. These are special cases of totally geodesic subgroups of diffeomorphisms with Lie algebras big enough to detect the vanishing of a symmetric 2-tensor field.
Keywords
Cite
@article{arxiv.math/0103220,
title = {Totally geodesic subgroups of diffeomorphisms},
author = {Stefan Haller and Josef Teichmann and Cornelia Vizman},
journal= {arXiv preprint arXiv:math/0103220},
year = {2009}
}