Classification theorems for biharmonic real hypersurfaces in a complex projective space

Abstract

First, we classify proper biharmonic Hopf real hypersurfaces in $\mathbb{C}{P}^2$. Next, we classify proper biharmonic real hypersurfaces with two distinct principal curvatures in $\mathbb{C}{P}^n$, where $n\ge 2$. Finally, we prove that biharmonic ruled real hypersurfaces in $\mathbb{C}{P}^n$ are minimal, where $n\ge 2$.