Communications of the
Korean Mathematical Society CKMS

In this paper, We characterize a semi-invariant submanifold of codimension 3 satisfying $\nabla_{\xi}A=0$ in a complex projective space ${\Bbb{C}}P^{n+1}$, where $\nabla_{\xi}A$ is the covariant derivative of the shape operator $A$ in the direction of the distinguished normal with respect to the structure vector field $\xi$.

Keywords: Semi-invariant submanifold, distinguished normal, shape operator, Hopf real hypersurface

MSC numbers: 53C25, 53C40, 53C42