A representation formula for indefinite improper affine spheres

2008/01/31 by Daisuke Nakajo, Nakajo, Daisuke · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.0801.4832

arxiv created 2008/01/31 · openalex publication_date 2008/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We 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.

Cited by

• A class of affine maximal surfaces with singularities and its relationship with minimal surface theory

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