A representation formula for indefinite improper affine spheres
Daisuke Nakajo
TL;DR
This paper introduces a new mathematical formula for indefinite improper affine spheres using para-holomorphic functions, analyzes their singularities, and compares this approach with existing formulas.
Contribution
The paper presents a novel representation formula for indefinite improper affine spheres and examines the nature of their singularities, notably excluding cuspidal cross caps.
Findings
Cuspidal cross caps do not appear as singularities on these spheres.
The new formula provides insights into the structure of indefinite improper affine spheres.
Comparison with other formulas highlights advantages of the new approach.
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.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Algebraic and Geometric Analysis · Digital Image Processing Techniques