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

Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures