2022/11/30 by Accornero, Luca, Cattafi, Francesco
#53C10 #58A15 #58H05 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2211.16639
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. We encode geometric structures induced by transitive Lie pseudogroups into principal G-bundles equipped with a transversally parallelisable foliation generated by a subalgebra of \mathfrakg, called Cartan bundles. Our approach is complementary to arXiv:1911.13147 and is based on Morita equivalence of Lie groupoids. After identifying the main examples and properties, we develop a notion of flatness with respect to a Lie algebra, which encompasses the classical integrability of G-structures, the flatness of Cartan geometries, as well as the integrability of contact structures.