2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146980We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions and study singularities which appear in this representation formula. As a result, it follows that cuspidal cross caps never appear as the singularities on indefinite improper affine spheres and so on. Comparison with other representation formulae are also studied.Differential Geometrytext