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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.

Lagrangian $H$-umbilical submanifolds in quaternion Euclidean spaces