Contributions to Algebra and Geometry

Vol. 39, No. 2, pp. 413-421 (1998)

Department of Applied Mathematics, South China Institute of Technology, Guangzhou, ChinaDepartment of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A

**Abstract:** Lagrangian submanifolds satisfying Chen's equality in a quaternion-space-form are investigated. In particular, we prove that (1) every Lagrangian submanifold of a quaternion-space-form satisfying Chen's equality must be minimal and (2) the only Lagrangian isometric immersion from a Riemannian $n$-sphere into a quaternionic projective space $P^n(H)$ satisfying Chen's equality is the totally geodesic one.

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