Minimal 5(2)-ideal Lagrangian submanifolds and the quaternionic projective space

We construct an explicit map from a generic minimal 5(2)-ideal Lagrangian submanifold of Cn to the quaternionic projective space HPn-1, whose image is either a point or a minimal totally complex surface. A stronger result is obtained for n = 3, since the above mentioned map then provides a one-to-one correspondence between minimal 5(2)-ideal Lagrangian submanifolds of C3 and minimal totally complex surfaces in HP2 which are moreover anti-symmetric. Finally, we also show that there is a one-to-one correspondence between such surfaces in HP2 and minimal Lagrangian surfaces in CP2.& COPY; 2023 Elsevier B.V. All rights reserved.