Bulletin of the
Korean Mathematical Society BKMS

In this paper we prove that if $M$ is a $J$-invariant submanifold of codimension $2$ in a complex projective space $P_{n+1} (C)$, and the second fundamental tensor is cyclic-parallel or $M$ has harmonic curvature, then $M$ is locally complex quadric $Q_n (C)$ or $P_n (C)$.

Keywords: $J$-invariant submanifold, complex projective space, cyclic-parallel, harmonic curvature

MSC numbers: 53C40, 53C15