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We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd‐dimensional spheres and certain Lagrangian surface belonging to a family that can be considered as a generalization of the special Lagrangian surfaces in complex Euclidean plane. Our examples include those invariant under the standard action of  SO ( p +1)× SO ( q +1) on C  n   = C  p +1  ×C  q +1 ,  n = p + q +2.

On a new construction of special Lagrangian immersions in complex Euclidean space