56 citations · 403 across the 41 of their papers we have counts for
42 papers
Haantjes torsion and integrability: a proof of Bolsinov-Konyaev-Matveev's conjecture
Alessandro Arsie, Paolo Lorenzoni
We prove a conjecture formulated by Bolsinov, Konyaev and Matveev in [7] stating that, integrability of a system of hydrodynamic type with $\mathfr…
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…
Miura-reciprocal transformations and localizable Poisson pencils
P. Lorenzoni, S. Shadrin, R. Vitolo
We show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain…
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…