Submanifolds with proper d-planar geodesics immersed in complex projective spaces (Q1081848)

An isometric immersion i of M into \(\overline{M}\) is called a d-planar geodesic immersion if each geodesic in M is mapped locally under i into a d-dimensional totally geodesic submanifold of \(\overline{M}\). A 3-planar geodesic immersion is called a cubic geodesic immersion if it is isotropic. In this paper, the authors study a proper d-planar geodesic Kählerian immersion of a Kähler manifold into a complex projective space with the standard Study metric and a proper cubic geodesic totally real immersion into \({\mathbb{C}}P^ m\). Several classification theorems in these respects are obtained.