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

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

2003-07-20

arxiv.org/abs/math/0307272v1

Balkan Journal of Geometry and Its Applications, Vol. 7, No. 2, 2002, pp. 87-136

Mathematics

Differential Geometry

35 pages

Scientific paper

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.

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