  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 $\mathbb{H}\mathrm{P}^{m-1}$.
