Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 39, No. 2, pp. 413-421 (1998)

Lagrangian Submanifolds of Quaternion Kaehlerian Manifolds Satisfying Chen's Equality

Yi Hong, Chorng Shi Houh

Department of Applied Mathematics, South China Institute of Technology, Guangzhou, China

Department 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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