# Focal radii of orbits

@article{Gorodski2017FocalRO, title={Focal radii of orbits}, author={Claudio Gorodski and Artur B. Saturnino}, journal={Linear and Multilinear Algebra}, year={2017}, volume={67}, pages={2082 - 2103} }

ABSTRACT We show that every effective action of a compact Lie group K on a unit sphere admits an explicit orbit whose principal curvatures are bounded from above by .

#### 2 Citations

Highly curved orbit spaces

- Mathematics
- Differential Geometry and its Applications
- 2019

Abstract It is known that the infimum of the sectional curvatures (on the regular part) of orbit spaces of isometric actions on unit spheres is bounded above by 4. We show that the infimum is 1 for… Expand

A diameter gap for quotients of the unit sphere

- Mathematics
- 2019

We prove that for any isometric action of a group on a unit sphere of dimension larger than one, the quotient space has diameter zero or larger than a universal dimension-independent positive… Expand

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