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Sobolev metrics on the manifold of all riemannian metrics

Martin Bauer Universit¨at Wien Philipp Harms Harvard University Peter W. Michor Universit¨at Wien

Differential Geometry mathscidoc:1609.10312

Journal of Differential Geometry, 94, (2), 187-208187-208, 2013
On the manifoldM(M) of all Riemannian metrics on a compact manifold M, one can consider the natural L2-metric as described first by [11]. In this paper we consider variants of this metric, which in general are of higher order. We derive the geodesic equations; we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition when Ricci flow is a gradient flow for one of these metrics.
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@inproceedings{martin2013sobolev,
  title={SOBOLEV METRICS ON THE MANIFOLD OF ALL RIEMANNIAN METRICS},
  author={Martin Bauer, Philipp Harms, and Peter W. Michor},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914075433656649974},
  booktitle={Journal of Differential Geometry},
  volume={94},
  number={2},
  pages={187-208187-208},
  year={2013},
}
Martin Bauer, Philipp Harms, and Peter W. Michor. SOBOLEV METRICS ON THE MANIFOLD OF ALL RIEMANNIAN METRICS. 2013. Vol. 94. In Journal of Differential Geometry. pp.187-208187-208. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914075433656649974.
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