# Totally Real Flat Minimal Surfaces in Quaternionic Projective Spaces

## TL;DR

This paper classifies totally real flat minimal surfaces in quaternionic projective spaces, showing they correspond to specific surfaces in complex projective spaces, including the Clifford solution, up to symplectic congruence.

## Contribution

It provides a classification of totally real flat minimal surfaces in quaternionic projective spaces, linking them to known surfaces in complex projective spaces and identifying the Clifford solution.

## Key findings

- Classification of totally real flat minimal surfaces in $ ext{HP}^n$
- Identification of surfaces as those in $ ext{CP}^n$
- Inclusion of the Clifford solution

## 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.