Tzitzéica transformation is a dressing action

Details Tzitzéica transformation is a dressing action Tzitzéica transformation is a dressing action

2006-05-15

arxiv.org/abs/math/0605404v1

J. Math. Phys. 47, 053502 (2006)

Mathematics

Differential Geometry

Scientific paper

10.1063/1.2195527

We classify the simplest rational elements in a twisted loop group, and prove
that dressing actions of them on proper indefinite affine spheres give the
classical Tzitz\'eica transformation and its dual. We also give the group point
of view of the Permutability Theorem, construct complex Tzitz\'eica
transformations, and discuss the group structure for these transformations.

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