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Cohomogeneity one actions on unit spheres (1707.02763v2)
Published 10 Jul 2017 in math.DG
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 $\mathbb{H}\mathrm{P}{m-1}$.