# The Riemannian geometry of orbit spaces. The metric, geodesics, and integrable systems

@article{Alekseevsky2001TheRG, title={The Riemannian geometry of orbit spaces. The metric, geodesics, and integrable systems}, author={Dmitry V. Alekseevsky and Andreas Kriegl and Mark V. Losik and Peter W. Michor}, journal={arXiv: Differential Geometry}, year={2001} }

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit strata which are more singular only at the end points. This is phrased as convexity result. The geodesic spray, viewed as a (strata-preserving) vector field on $TM/G$, leads to the notion of geodesics in $M/G$ which are projections under $M\to M/G$ of geodesics…

## 4 Citations

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