Lagrangian $H$-umbilical submanifolds in quaternion Euclidean spaces

Abstract

In [2], B. Y. Chen proved that the Lagrangian $H$-umbilical submanifolds in complex Euclidean space C$^{n}$ are Lagrangian pseudospheres and complex extensors of the unit hypersphere of E$^{n}$, except the flat ones. Similar to this, we can define the Lagrangian $H$-umbilical submanifold in quatemion space forms. The main purpose of this paper is to classify the Lagrangian $H$-umbilical submanifolds in quatemion Euclidean space H$^{n}$.