Weierstraß-type representation of affine spheres

Weierstraß-type representation of affine spheres

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 c...

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Veröffentlicht in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2001-01, Vol.71 (1), p.225-250
Hauptverfasser: Dorfmeister, J., Eitner, U.
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
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Zusammenfassung: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.
ISSN:0025-5858
1865-8784
DOI:10.1007/BF02941473