Communications of the
Korean Mathematical Society CKMS

The purpose of this paper is to give some characterizations of $n$-dimensional $CR$-submanifolds of $(n-1)$ $CR$-dimension immersed in a complex projective space $CP^{(n+p)/2}$ with Fubini-Study metric and we study an $n$-dimensional compact, orientable, minimal $CR$-submanifold of $(n-1)$ $CR$-dimension in $CP^{(n+p)/2}$.

Keywords: $CR$-submanifold, $CR$-dimension, Maximal $J$-invariant subspace, Shape operator, Normal, Minimal

MSC numbers: 53C40 , 53C42