Abstract We conclude the classification of cohomogeneity one actions on symmetric spaces rank by classifying quaternionic hyperbolic up to orbit equivalence. As a by-product our proof, we produce uncountably many examples inhomogeneous isoparametric families hypersurfaces with constant principal curvatures in spaces.

Special Lagrangian submanifolds of complex Euclidean space C have been studied widely over the last few years. These submanifolds are volume minimizing and, in particular, they are minimal submanifolds. When n = 2, special Lagrangian surfaces of C are exactly complex surfaces with respect to another orthogonal complex structure on R ≡ C. A very important problem here, and even a good starting p...