Cohomogeneity one actions on unit spheres

Abstract

In this paper, we provide a complete classification for all the isometric cohomogeneity one actions on unit spheres. Using this theory, we can very easily classify all the isometric cohomogeneity one actions on the Riemannian symmetric spaces $\mathbb{C}{\mathrm{P}}^{m-1}$ and $\mathbb{H}{\mathrm{P}}^{m-1}$.

The author has recently found the reference which had provided the full classification of cohomogeneity one actions on unit spheres