Minimal submanifolds of E 2 n + 1 E^ {2n+1} arising from degenerate SO ( 3 ) extrm {SO} (3) orbits on the Grassmannian Academic Article

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