The explicit representation of flat 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 are Lagrangian pseudo-spheres and complex extensors of the unit hypersphere of E, except the flat ones. Similar to this, we can define the Lagrangian H-umbilical submanifold in quaternion space forms. The main purpose of this paper is to classify the Lagrangian H-umbilical submanifolds in quaternion Euclidean space H.