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arXiv · 2208.14817

Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures

Paolo Lorenzoni·Sara Perletti
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Abstract

Combining the construction of integrable systems of hydrodynamic type starting from the Fr\"olicher-Nijenhuis bicomplex $(d,d_L)$ associated with a (1,1)-tensor field $L$ with vanishing Nijenhuis torsion with the construction of flat structures starting from integrable systems of hydrodynamic type we define multi-parameter families of bi-flat structures $(\nabla,e,\circ,\nabla^*,*,E)$ associated with Fr\"olicher-Nijenhuis bicomplexes. We call these structures Lauricella bi-flat structures since in the n-dimensional semisimple case (n-1) flat coordinates of r are Lauricella functions.

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Paolo Lorenzoni, Sara Perletti. 2022-08-31. Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures. https://doi.org/10.1088/1361-6544%2Fad05dc

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