Moving frames and Clifford algebras will be used to illustrate an interconnected approach to the study of integrable systems, their surfaces, and methods for producing integrable partial differential equations. After a system of one-forms is defined, moving frame equations can be integrated and the resulting equations for the surface can be obtained. Other differential equations which involve quantities relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case of constant mean curvature, they can be expressed in terms of Jacobi elliptic functions.
Paul Bracken, "Cartan frames and algebras with links to integrable systems differential equations and surfaces", J. Math. Phys. 59, 021504 (2018) https://doi.org/10.1063/1.5005816
Journal of Mathematical Physics