56 citations · 403 across the 41 of their papers we have counts for
4 papers · 2 filters
Darboux-Egorov system, bi-flat -manifolds and Painlevé VI
Paolo Lorenzoni
This is a generalization of the procedure presented in [3] to construct semisimple bi-flat -manifolds starting from homogeneous solut…
Reciprocal -manifolds
Alessandro Arsie, Paolo Lorenzoni
We consider the action of a special class of reciprocal transformation on the principal hierarchy associated to a semisimple -manifold with compatible flat structure $(M,\circ,\…
Poisson bracket on 1-forms and evolutionary partial differential equations
Alessandro Arsie, Paolo Lorenzoni
We introduce a bracket on 1-forms defined on , the infinite jet extension of the space of loops and prove that it satisfies the standard prope…
From Darboux-Egorov system to bi-flat -manifolds
Alessandro Arsie, Paolo Lorenzoni
Motivated by the theory of integrable PDEs of hydrodynamic type and by the generalization of Dubrovin's duality in the framework of -manifolds due to Manin [22], we consider a s…