A Weierstrass-Type Representation for Maximal Surfaces in the Five-Dimensional Minkowski Space ℝ15

Abstract

We develop a Weierstrass-type representation for conformal maximal surfaces in the five-dimensional Minkowski space [Formula: see text]. The construction extends the classical representation theory for maximal surfaces in [Formula: see text] and its higher-codimensional analogues by producing explicit holomorphic data generating isotropic complex differentials in Lorentzian signature [Formula: see text]. We also derive an integral-free formulation based on a single holomorphic seed function, giving an explicit reconstruction procedure analogous to classical lower-dimensional cases. Several examples are computed, including polynomial and exponential families, and degeneracy loci are described explicitly. The role of the Lorentzian metric is analyzed in detail.