Science China Mathematics

, Volume 57, Issue 7, pp 1505–1516 | Cite as

The noncommutative KdV equation and its para-Kähler structure

  • Qing DingEmail author
  • ZhiZhou He


We prove that the noncommutative (n × n)-matrix KdV equation is exactly a reduction of the geometric KdV flows from ℝ to the symmetric para-Grassmannian manifold \(\tilde G_{2n,n} \) = SL(2n, ℝ)/SL(n, ℝ) × SL(n, ℝ) and it can also be realized geometrically as a motion of Sym-Pohlmeyer curves in the symmetric Lie algebra sl(2n, ℝ) with initial data being suitably restricted. This gives a para-geometric characterization of the noncommutative matrix KdV equation.


para-Kähler structure noncommutative KdV geometric realization 


37K25 37K10 53C44 58G30 


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© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina

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