230 citations · 391 across the 17 of their papers we have counts for
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Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds
Mario Micheli, Peter W. Michor, David Mumford
Given a finite dimensional manifold , the group of diffeomorphism of which fall suitably rapidly to the identity, acts on the manifold…
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
Peter W. Michor, David Mumford
Here shape space is either the manifold of simple closed smooth unparameterized curves in or is the orbifold of immersions from to modulo the grou…
Reflection groups on Riemannian manifolds
Dmitri Alekseevsky, Andreas Kriegl, Mark Losik +1
We investigate discrete groups of isometries of a complete connected Riemannian manifold which are generated by reflections, in particular those generated by disecting refl…
On the curvature of a certain Riemannian space of matrices
Attila Andai, Peter W. Michor, Denes Petz
The curvature tensor and the scalar curvature are computed in the space of positive definite real matrices endowed by the Kubo-Mori inner product as a Riemannian metric.
Description of infinite dimensional abelian regular Lie groups
Peter W. Michor, Josef Teichmann
It is shown that every abelian regular Lie group is a quotient of its Lie algebra via the exponential mapping.
Poisson structures on double Lie groups
D. Alekseevsky, J. Grabowski, G. Marmo +1
Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin- and Gauß-decompositions. The standard R-matrix in a Manin decomposition then gi…
Regular infinite dimensional Lie groups
Andreas Kriegl, Peter W. Michor
Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolutio…
Product preserving functors of infinite dimensional manifolds
Andreas Kriegl, Peter W. Michor
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of -algebras.
Differential geometry of -manifolds
Dimitri Alekseevsky, Peter W. Michor
An action of a Lie algebra on a manifold is just a Lie algebra homomorphism . We define orbits for such an action. In general the space of or…