Submanifolds of quaternion projective space with bounded second fundamental form

抄録

Let h be the second fundamental form of a compact submanifold M of the quaternion projective space HPⁿ(1). For any unit vector u∈TM, set δ(u)=||h(u, u)||². We determine all compact totally complex submanifolds of HPⁿ(1) (resp. all compact totally real minimal submanifolds of HPⁿ(1)) satisfying condition δ(u){≤}¼ (resp. δ(u){≤}\frac{1}{12}) unit vectors u∈TM.