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