Orthogonal complex structures in $\mathbb{R}^4$

Orthogonal complex structures in domains in $\mathbb{R}^4$ are studied using methods of multidimensional complex analysis. New results on removable singularities of such structures are established. The simplest multivalued orthogonal complex structures are investigated. A classification of quadrics in $\mathbb{CP}_3$ with respect to the action of the conformal group is given, and the discriminant sets of the twistor projections of model quadrics are described.
Bibliography: 39 titles.