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Sectional Curvature in terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
shape spaces landmark points cometric sectional curvature
2010/12/6
This paper deals with the computation of sectional curvature for the manifolds of N land-
marks (or feature points) in D dimensions, endowed with the Riemannian metric induced by the
group action of...
The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature
Cross curvature flow geometric evolution equation negative sectional curvature monotonicity formula hyperbolic metric
2010/2/26
We consider the cross curvature flow, an evolution equation of metrics on 3-manifolds. We establish short time existence when the sectional curvature has a sign. In the case of negative sectional curv...