Abstract
Affine spheres are discussed in the context of loop groups. We show that every affine sphere can be obtained by solving two ordinary differential equations followed by an application of a generalized Birkhoff Decomposition Theorem (which we proof in the Appendix). A geometric interpretation of the coefficients of the ODE is given. Finally the method is applied to construct all ruled surfaces.
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Most of this work was done while the second named author was visiting the University of Kansas.
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Dorfmeister, J., Eitner, U. Weierstraß-type representation of affine spheres. Abh.Math.Semin.Univ.Hambg. 71, 225–250 (2001). https://doi.org/10.1007/BF02941473
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DOI: https://doi.org/10.1007/BF02941473