Minimal submanifolds of $E^ {2n+1}$ arising from degenerate $\textrm {SO} (3)$ orbits on the Grassmannian

Abstract:

We give new examples of minimal submanifolds of ${{\mathbf {E}}^{2n + 1}}$ characterised by having their Gauss map’s image lie in degenerate $SO(3)$ orbits of ${G_{p,2n + 1}}$, the Grassmannian of $p$-planes in ${{\mathbf {E}}^{2n + 1}}$ (where the action on ${G_{p,2n + 1}}$ is induced from the irreducible $SO(3)$ action on ${{\mathbf {R}}^{2n + 1}}$). These submanifolds are all given explicitly in terms of holomorphic data and are linearly full in ${{\mathbf {E}}^{2n + 1}}$.