Communications of the
Korean Mathematical Society CKMS

This paper has two objectives. The first objective is to study slant submanifolds of quaternion Kaehler manifolds. We give characterization theorems and examples of slant submanifolds. For the second objective, we introduce the notion of semi-slant submanifolds which are different from the definition of N. Papaghiuc \cite{Papa}. We obtain characterization theorems, examples of semi-slant submanifolds and investigate the geometry of leaves of distributions which are involved in the definition of semi-slant submanifolds.

Keywords: slant submanifold, semi-slant submanifold, {\bf $QR$}-submanifold, quaternion Kaehler manifold

MSC numbers: 53C15, 53C40