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Many integrable systems can be reformulated as holomorphic vector bundles on twistor space.
K. Costello and M. Yamazaki, Gauge theory and integrability, III , 1908.02289
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K. Costello, “Topological strings, twistors, and skyrmions.” Available at http://web.math.ucsb.edu/~drm/WHCGP/ (4/27/2020)
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R.F. Penna, Einstein–Rosen waves and the Geroch group , Journal of Mathematical Physics 62
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