The completion of the manifold of riemannian metrics

Brian Clarke Universit¨at M¨unster

Differential Geometry mathscidoc:1609.10298

Journal of Differential Geometry, 93, (2), 203-268, 2013
We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finitedimensional, orientable manifold with respect to a natural metric called the L2 metric. The primary motivation for studying this problem comes from Teichm¨uller theory, where similar considerations lead to a completion of the well-known Weil-Petersson metric. We give an application of the main theorem to the completions of Teichm¨uller space with respect to a class of metrics that generalize the Weil-Petersson metric.
No keywords uploaded!
[ Download ] [ 2016-09-14 07:37:21 uploaded by admin ] [ 592 downloads ] [ 0 comments ] [ Cited by 8 ]
@inproceedings{brian2013the,
  title={THE COMPLETION OF THE MANIFOLD OF RIEMANNIAN METRICS},
  author={Brian Clarke},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914073721562708960},
  booktitle={Journal of Differential Geometry},
  volume={93},
  number={2},
  pages={203-268},
  year={2013},
}
Brian Clarke. THE COMPLETION OF THE MANIFOLD OF RIEMANNIAN METRICS. 2013. Vol. 93. In Journal of Differential Geometry. pp.203-268. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914073721562708960.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved