Focal radii of orbits

  title={Focal radii of orbits},
  author={Claudio Gorodski and Artur B. Saturnino},
  journal={Linear and Multilinear Algebra},
  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
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 forExpand
A diameter gap for quotients of the unit sphere
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 positiveExpand


The curvature of orbit spaces
We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.
On orbit spaces of representations of compact Lie groups
We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotientsExpand
Diameters of spherical Alexandrov spaces and curvature one orbifolds
Let G be a closed, non-transitive subgroup of O(n+1), where n ≥ 2, and let Q = S/G. We will show that for each n there is a lower bound for the diameter of Q. If G is finite then Q is an orbifold ofExpand
Diameters of 3-sphere quotients
Abstract Let G ⊂ O ( 4 ) act isometrically on S 3 . In this article we calculate a lower bound for the diameter of the quotient spaces S 3 / G . We find it to be 1 2 arccos ( tan ( 3 π 10 ) 3 ) ,Expand
Nonnegatively and Positively curved manifolds
The aim of this paper is to survey some results on nonnegatively and positively curved Riemannian manifolds. One of the important features of lower curvature bounds in general is the invariance underExpand
The diameter function on the space of space form
© Foundation Compositio Mathematica, 1993, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: // implique l’accord avec les conditionsExpand
New extremal problems for the Riemannian recognition program via Alexandrov geometry
In its most general form, the recognition problem in riemannian geometry asks for the identification of an unknown riemannian manifold via measurements of metric invariants on the manifold. OptimallyExpand
Submanifolds and Holonomy
Basics of Submanifold Theory in Space Forms The fundamental equations for submanifolds of space forms Models of space forms Principal curvatures Totally geodesic submanifolds of space forms ReductionExpand
The curvature of orbit spaces , To appear in Geom . Dedicata . [ GL 14 ] , On orbit spaces of representations of compact Lie groups
  • J . reine angew . Math .
  • 2014