Weierstrass representations for triply orthogonal and conformal Euclidean and Lorentzian systems (Q2176075)

The paper under review deals with triply orthogonal systems in the three-dimensional Euclidean and Lorentz-Minkowski spaces [\textit{B. A. Shipman} et al., J. Geom. 108, No. 2, 545--563 (2017; Zbl 1377.53007)]. As the main result, Weierstrass-type representations for such systems are constructed and the Gauss and mean curvatures of coordinate surfaces are expressed in terms of Weierstrass data. Besides, Weierstrass data corresponding to triply conformal systems are studied and their relations to generalized Möbius transformations are discussed.