The Weierstrass representation of closed surfaces in ℝ3

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 1998Embargo end date: 01 Jan 1997 English Publisher:Springer Science and Business Media LLCJournal:Functional Analysis and Its Applications, volume 32, pages 258-267 (issn: 0016-2663, eissn: 1573-8485,

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Authors: Taimanov, Iskander A.;

doi: 10.1007/bf02463208 , 10.48550/arxiv.dg-ga/9710020

arXiv: dg-ga/9710020

The Weierstrass representation of closed surfaces in ℝ3

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Abstract

In the present paper which a sequel to dg-ga/9511005 and dg-ga//9610013 a global Weierstrass representation of an arbitrary closed oriented surface of genus $\geq 1$ in the the three-space is constructed. The Weierstrass spectrum of a torus immersed into $R^3$ is introduced and finite-zone planes as well as finite-zone solutions to the modified Novikov-Veselov equations are constructed.

15 pages, LaTeX; Preprint no. 291, SFB 288, TU-Berlin

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics

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