In the present paper, we describe the conformal immersion of the surface into R4 by means of a linear system. Furthermore we prove that every regular conformal immersion of a surface into R4 is locally determined by the generalized Weierstrass formulae. We also give the representation of the surface with parallel mean curvature vector by solutions with the parameter of a linear system which is determined by the sinh-Laplace equation. © 2006 Elsevier Ltd. All rights reserved.
Chen, J., & Chen, W. (2007). Generalized Weierstrass representation of surfaces in R4. Journal of Geometry and Physics, 57(2), 367–378. https://doi.org/10.1016/j.geomphys.2006.02.013