Totally Real Flat Minimal Surfaces in Quaternionic Projective Spaces

Abstract

In this paper, we study totally real minimal surfaces in the quaternionic projective space $\mathbb{H}{P}^n$. We prove that the linearly full totally real flat minimal surfaces of isotropy order $n$ in $\mathbb{H}{P}^n$ are two surfaces in $\mathbb{C}{P}^n$, one of which is the Clifford solution, up to symplectic congruence.