Abstract.
We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions. Affie spheres which are obtained by this formula may have singularities. Recently, useful criteria for cuspidal edges, swallowtails and cuspidal cross caps are given in [8] and [4]. Using them, we study singularities which appear in this representation formula. As an exemplary result it follows that cuspidal cross caps never appear as the singularities on indefinite improper affine spheres. We compare our representation with other representation formulae in the literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: December 18, 2007. Revised: March 24, 2009. Accepted: March 26, 2009.
Rights and permissions
About this article
Cite this article
Nakajo, D. A Representation Formula for Indefinite Improper Affine Spheres. Results. Math. 55, 139–159 (2009). https://doi.org/10.1007/s00025-009-0399-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-009-0399-4