56 citations · 403 across the 41 of their papers we have counts for
6 papers · 1 filter
Bi-flat F-structures as differential bicomplexes and Gauss-Manin connections
Alessandro Arsie, Paolo Lorenzoni
We show that a bi-flat F-structure on a manifold defines a differential bicomplex on forms with value on the t…
Regular non-semisimple Dubrovin-Frobenius manifolds
Paolo Lorenzoni, Sara Perletti
We study regular non-semisimple Dubrovin-Frobenius manifolds in dimensions 2,3,4. We focus on the case where the Jordan canonical form of the operator of multiplication by the Eule…
A Dubrovin-Frobenius manifold structure of NLS type on the orbit space of
Alessandro Arsie, Paolo Lorenzoni, Igor Mencattini +1
Generalizing a construction presented in [3], we show that the orbit space of less the image of coordinate lines under the quotient map is equipped with two Dubrovin-Frobeniu…
Riemannian F-manifolds, bi-flat F-manifolds, and flat pencils of metrics
Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni +1
In this paper we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold we present a construction of a canonical…
Hamiltonian operators of Dubrovin-Novikov type in 2D
E. V. Ferapontov, P. Lorenzoni, A. Savoldi
First order Hamiltonian operators of differential-geometric type were introduced by Dubrovin and Novikov in 1983, and thoroughly investigated by Mokhov. In 2D, they are generated b…
-manifolds and integrable systems of hydrodynamic type
Paolo Lorenzoni, Marco Pedroni, Andrea Raimondo
We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In su…