Séminaire animé par Peter W. Michor (Universität Wien)
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ABSTRACT:
On the space Emb of all smooth embeddings (more general: immersions) from a compact manifold M into a Riemannian manifold (N,g ) act the Lie group of all diffeomorphisms of M from the right, and various groups of diffeomorphisms of N from the left. Quotiening out the right action leads to a prime example of shape space, also called the nonlinear Grassmannian, consisting of all submanifolds of N of type M.
Invariant Riemannian metrics on Emb lead to Riemannian metrics on shape space, whose geodesic distances can be used to differentiate between shapes, and whose curvatures affect statistics of shapes.
The left action, via right invariant Riemannian metrics on the diffeomorphism groups of N, also induces various metrics on shape spaces which have found many applications from paelontology to computational anatomy.
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