10 citations · 20 across the 5 of their papers we have counts for
9 papers · 1 filter
Riemannian geometries on spaces of plane curves
Peter W. Michor, David Mumford
We study some Riemannian metrics on the space of regular smooth curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms o…
Completing Lie algebra actions to Lie group actions
Franz W. Kamber, Peter W. Michor
For a finite dimensional Lie algebra $\g$ of vector fields on a manifold we show that can be completed to a -space in a unversal way, which however is neither Hausdorff…
Tensor fields and connections on holomorphic orbit spaces of finite groups
Andreas Kriegl, Mark Losik, Peter W. Michor
For a representation of a finite group on a complex vector space we determine when a holomorphic -tensor field on the principle stratum of the orbit space $V/…
The Riemannian geometry of orbit spaces. The metric, geodesics, and integrable systems
Dmitry Alekseevsky, Andreas Kriegl, Mark Losik +1
We investigate the rudiments of Riemannian geometry on orbit spaces for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minim…
The flow completion of a manifold with vector field
Franz W. Kamber, Peter W. Michor
For a vector field on a smooth manifold there exists a smooth but not necessarily Hausdorff manifold and a complete vector field on it which is the un…
Extensions of Lie algebras
Dmitri Alekseevsky, Peter W. Michor, Wolfgang Ruppert
We review (non-abelian) extensions of a given Lie algebra, identify a 3-dimensional cohomological obstruction to the existence of extensions. A striking analogy to the setting of c…