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Weierstrass-type Representation of Weakly Regular Pseudospherical Surfaces in Euclidean Space

Differential Geometry 2007-05-23 v1 Analysis of PDEs

Abstract

The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given representation, constitutes the subject of a separate, ulterior report. The appendix of the present work gives an elementary proof of the Birkhoff decomposition theorem for "loop-groups" of spectral parameter based on the real line, instead of the unit circle.

Keywords

Cite

@article{arxiv.math/0307272,
  title  = {Weierstrass-type Representation of Weakly Regular Pseudospherical Surfaces in Euclidean Space},
  author = {Magdalena Toda},
  journal= {arXiv preprint arXiv:math/0307272},
  year   = {2007}
}

Comments

35 pages

R2 v1 2026-07-22T16:56:24.895Z