The exceptional compact symmetric spaces \(G_2\) and \(G_2/\text{SO}(4)\) as tubes
The author studies cohomogeneity one actions of \(\text{SU}(3)\times \text{SU}(3)\) on the exceptional Lie group \(G_2\) and of \(\text{SU}(3)\) on the symmetric space \(G_2/\text{SO}(4)\). He computes the principal curvatures of the principal orbits and rederives the volume of \(G_2\) and \(G_2/\text{SO}(4)\).
scientific article; zbMATH DE number 2111517