Survey on real forms of the complex A2(2)-Toda equation and surface theory

@article{Dorfmeister2019SurveyOR,
  title={Survey on real forms of the complex A2(2)-Toda equation and surface theory},
  author={Josef F. Dorfmeister and Walter Freyn and Shimpei Kobayashi and Erxiao Wang},
  journal={Complex Manifolds},
  year={2019},
  volume={6},
  pages={194 - 227}
}
The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop parameter. As a matter of fact, the same result holds for $k$-symmetric spaces over reductive Lie groups. In this survey we will show that to each of the five different types of real forms for a loop group of $A_2^{(2)}$ there exists a surface class, for… CONTINUE READING
1
Twitter Mention

References

Publications referenced by this paper.
SHOWING 1-10 OF 43 REFERENCES

Sur une nouvelle classe des surfaces

G. Tzitzéica
  • C. R. Acad. Sci. Paris, 150:955–956
  • 1910
VIEW 14 EXCERPTS
HIGHLY INFLUENTIAL

Concerning Surfaces with constant negative curvature

A. V. Bäcklund
  • New Era Printing Co., Lancaster, PA, 1905.
  • 1883
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

De nite a ne spheres via loop groups I: general theory

J. F. Dorfmeister, E. Wang
  • preparation
  • 2019
VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space

Josef F. Dorfmesiter, Shimpei Kobayashi
  • 2019
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Totally Real Minimal Tori in Cp

VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

De nite a ne spheres via loop groups II: equivariant solutions

J. F. Dorfmeister, E. Wang
  • preparation
  • 2019
VIEW 1 EXCERPT

Some new examples of minimal Lagrangian surfaces in CP2

J. F. Dorfmeister, H. Ma
  • preparation
  • 2019
VIEW 1 EXCERPT