Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions
The authors obtain a Weierstrass-type formula for conformal Lagrangian immersions in Euclidean 4-space and show that the data satisfies a Dirac-type equation. They also propose an equivalent representation using quaternions, much simpler to handle in the case of Hamiltonian stationary Lagrangian immersions. As applications, they investigate immersed Klein bottles in the above family, classifying them and showing that they self-intersect.
scientific article; zbMATH DE number 1562865