An infinite number of hidden variables in hyper‐Kähler metrics

@inproceedings{Takasaki1989AnIN,
  title={An infinite number of hidden variables in hyper‐K{\"a}hler metrics},
  author={Kanehisa Takasaki},
  year={1989}
}
Three types of hidden variables, both independent and dependent, are shown to underlie the hyper‐Kahler geometry in a complexified setting. The variables satisfy an infinite set of differential equations (‘‘hierarchy’’), just as in the case of most nonlinear integrable systems. The notion of the Plebanski key functions [J. Math. Phys. 16, 2395 (1975)] is extended to this hierarchy to give an analog of the notion of the ‘‘τ function.’’ Two examples of special solutions, which are reminiscent of… CONTINUE READING

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