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 in bounded above by $4$. We show that the infimum is $1$ for "most" actions, and determine the cases in which it is bigger than $1$.

4 pages, 2 figures

References in corpus (2)

• Finite-Dimensional Lie Algebras and Their Representations for Unified Model Building
• Homogeneity rank of real representations of compact Lie groups