Classification results for totally real surfaces of nearly Kähler $\mathbb{C}{P}^3$

Abstract

Totally real surfaces in the nearly Kähler $\mathbb{C}{P}^3$ are investigated and are completely classified under various additional assumptions, resulting in multiple new examples. Among others, the classification includes totally real surfaces that are extrinsically homogeneous; or minimal; or totally umbilical; or Codazzi-like (including parallel and non-parallel examples).