Isothermic surfaces: conformal geometry, Clifford algebras and integrable systems
By F. Burstall. 2000
117 citations recorded by the source corpus.
We give an account of the classical and integrable geometry of isothermic surfaces in arbitrary co-dimension. We show that the classical transformation theory of Darboux, Bianchi and Calapso goes through unchanged in arbitrary co-dimension as does the connection with the "curved flats" of Ferus and Pedit. Moreover, we identify Darboux transformations with the dressing action of "simple factors" in the sense of Terng and Uhlenbeck. In so doing, we advertise the use of Vahlen's Clifford algebra matrices as an efficient computational tool in conformal geometry.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0e56de7d6a59401ba0910caac957312c0cb7af98
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Isothermic Surfaces in Spaces of Arbitrary Dimension: Integrability, Discretization, and Bäcklund Transformations—A Discrete Calapso Equation (2001, background): “An independent and detailed investigation of the geometry of isothermic surfaces in m and their transformation properties has recently been conducted by Burstall [23, 24].”