Totally real surfaces in the complex 2-space (Q2733925)

Let \(M\) be an immersed oriented surface in \(\mathbb{C}^2=( \mathbb{R}^4,\langle , \rangle,J)\), \(\langle , \rangle\) the standard inner product, \(J\) the standard almost complex structure on \(\mathbb{R}^4\). It is shown that any totally real conformal immersion from \(M\) into \(\mathbb{C}^2\) can be given by an algebraic combination of the components of a solution of a linear system of ODE's that is a Dirac-type equation on \(M\), given by the Kähler and Lagrange angle functions for the constructed \(M\). This representation entails a new construction method for surfaces in \(\mathbb{R}^4\).NEWLINENEWLINEFor the entire collection see [Zbl 0966.00031].