Transformations between surfaces in R^4 with flat normal and/or tangent   bundles
  We exhibit several transformations of surfaces in R^4. First, one that takes a flat surface and gets a surface with flat normal bundle; then, one that takes a surface with flat normal bundle and gets a flat surface; finally, a one-parameter family of transformations on a flat surface with flat normal bundle and gives a flat surface with flat normal bundle. This family satisfies a permutability property. 
Angel Montesinos-Amilibia