230 citations · 391 across the 17 of their papers we have counts for
17 papers
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…
Differentiable perturbation of unbounded operators
Andreas Kriegl, Peter W. Michor
If is a $C^{1,\al}$-curve of unbounded self-adjoint operators with compact resolvents and common domain of definition, then the eigenvalues can be parameterized in …
The generalized Cayley map from an algebraic group to its Lie algebra
Bertram Kostant, Peter W. Michor
Each infinitesimally faithful representation of a reductive complex connected algebraic group induces a dominant morphism from the group to its Lie algebra $\g$ by orthogon…
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.
Construction of completely integrable systems by Poisson mappings
J. Grabowski, G. Marmo, P. W. Michor
Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples ar…
Some remarks on the Pluecker relations
Mike Eastwood, Peter W. Michor
The Pluecker relations are equations which describe decomposable multivectors in . We review all known versions, give some new ones, and decompose them into irreducibl…
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…
Choosing roots of polynomials smoothly
Dmitri Alekseevsky, Andreas Kriegl, Mark Losik +1
We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are give…
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.
Basic differential forms for actions of Lie groups
Peter W. Michor
A section of a Riemannian -manifold is a closed submanifold which meets each orbit orthogonally. It is shown that the algebra of -invariant differential forms on …
Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions
Dmitri V. Alekseevsky, Janusz Grabowski, Giuseppe Marmo +1
On a cotangent bundle $T\sp*G$ of a Lie group one can describe the standard Liouville form and the symplectic form in terms of the right Maurer Cartan form and the le…
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…
The Frölicher-Nijenhuis bracket in non-commutative differential geometry
Andreas Cap, Andreas Kriegl, Peter W. Michor +1
We carry over to a quite general noncommutative setting some of the basic tools of differential geometry, using from the very beginning the setting of convenient vector spaces deve…