Sectional Curvature in Terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks

@article{Micheli2012SectionalCI,
  title={Sectional Curvature in Terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks},
  author={Mario Micheli and Peter W. Michor and David Mumford},
  journal={SIAM J. Imaging Sci.},
  year={2012},
  volume={5},
  pages={394-433}
}
This paper deals with the computation of sectional curvature for the manifolds of $N$ landmarks (or feature points) in $D$ dimensions, endowed with the Riemannian metric induced by the group action of diffeomorphisms. The inverse of the metric tensor for these manifolds (i.e., the cometric), when written in coordinates, is such that each of its elements depends on at most $2D$ of the $ND$ coordinates. This makes the matrices of partial derivatives of the cometric very sparse in nature, thus… 
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