Extension of symmetries on Einstein manifolds with boundary
Differential Geometry
2013-05-09 v6
Abstract
We investigate the validity of the isometry extension property for (Riemannian) Einstein metrics on manifolds with boundary. Given a metric on the boundary, this is the issue of whether any Killing field of the boundary metric extends to a Killing field of any bulk or filling Einstein metric inducing the given data on the boundary. Under a mild condition on the fundamental group, this is proved to be the case at least when the Killing field preserves the mean curvature of the boundary.
Keywords
Cite
@article{arxiv.0704.3373,
title = {Extension of symmetries on Einstein manifolds with boundary},
author = {Michael T. Anderson},
journal= {arXiv preprint arXiv:0704.3373},
year = {2013}
}
Comments
Correction to proof of main result given in new Appendix