8 citations · 13 across the 7 of their papers we have counts for
7 papers
Sub-Riemannian structures and non-transitive Cartan geometries via Lie groupoids
Ivan Beschastnyi, Francesco Cattafi, João Nuno Mestre
In this paper we discuss how to associate a suitable non-transitive version of a Cartan connection to sub-Riemannian manifolds of corank 1 (including contact and quasi-contact sub-…
PB-groupoids vs VB-groupoids
Alfonso Garmendia, Francesco Cattafi
In this paper we establish the principal bundle counterpart of the well-known and widely applied notion of vector bundle groupoid (VB-groupoid). In particular, we provide a general…
Pseudogroups of symmetries and Morita equivalences
Luca Accornero, Francesco Cattafi
This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective.…
A groupoid approach to transitive differential geometry
Luca Accornero, Francesco Cattafi
This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective.…
Cartan geometries and multiplicative forms
Francesco Cattafi
In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads u…
From PDEs to Pfaffian fibrations
Francesco Cattafi, Marius Crainic, Maria Amelia Salazar
We explain how to encode the essential data of a PDE on jet bundle into a more intrinsic object called Pfaffian fibration. We provide motivations to study this new notion and show…
Variational derivatives in locally Lagrangian field theories and Noether--Bessel-Hagen currents
Francesco Cattafi, Marcella Palese, Ekkehart Winterroth
The variational Lie derivative of classes of forms in the Krupka's variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser t…