Willmore Lagrangian Spheres in the Complex Euclidean Space Cn

In this paper we construct many examples of n-dimensionalWillmore Lagrangian submanifolds in the complex Euclidean space Cn. We characterize them as the only Willmore Lagrangian submanifolds invariant under the action of SO(n). The mostimportant contribution of our construction is that it provides examplesof Willmore Lagrangian spheres in Cnfor all n≥ 2.