14 citations · 16 across the 3 of their papers we have counts for
6 papers · 1 filter
A Note on Proper Poisson Actions
Rui Loja Fernandes
We show that the fixed point set of a proper action of a Lie group on a Poisson manifold by Poisson automorphisms has a natural induced Poisson structure and we give severa…
Rigidity and Flexibility in Poisson Geometry
Rui Loja Fernandes, Marius Crainic
We discuss several rigidity and flexibility phenomena in the context of Poisson geometry.
Invariants of Lie algebroids
Rui L. Fernandes
Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.
Integrability of Lie brackets
Marius Crainic, Rui L. Fernandes
In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controll…
Lie Algebroids, Holonomy and Characteristic Classes
Rui Loja Fernandes
We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural exte…
Connections in Poisson Geometry I: Holonomy and Invariants
Rui Loja Fernandes
We discuss contravariant connections on Poisson manifolds. For vector bundles, the corresponding operational notion of a contravariant derivative had been introduced by Izu Vaisman…