4 citations · 7 across the 9 of their papers we have counts for
9 papers · 1 filter
Stratified vector fields on orbit spaces
Mateus de Melo, Juan Sebastian Herrera-Carmona, Fabricio Valencia
Using Morita type stratifications, we establish a one-to-one correspondence between geometric vector fields on a separated differentiable stack and stratified vector fields on its…
Novikov type inequalities for orbifolds
Fabricio Valencia
We propose a natural extension of the Novikov numbers for the basic cohomology class of a closed basic -form on a proper Lie groupoid of finitely generated type. As an applicati…
Isometric Lie 2-group actions on Riemannian groupoids
Juan Sebastian Herrera-Carmona, Fabricio Valencia
We study isometric actions of Lie -groups on Riemannian groupoids by exhibiting some of their immediate properties and implications. Firstly, we prove an existence result which…
Morse theory on Lie groupoids
Cristian Ortiz, Fabricio Valencia
In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of M…
Invariant generalized almost complex structures on real flag manifolds
Fabricio Valencia, Carlos Varea
We characterize those real flag manifolds that can be endowed with invariant generalized almost complex structures. We show that no -maximal real flag manifolds admit integra…
Left invariant special Kähler structures
Fabricio Valencia
We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähle…
Invariant generalized complex geometry on maximal flag manifolds and their moduli
Elizabeth Gasparim, Fabricio Valencia, Carlos Varea
We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized Kähler structures on maximal flag manifolds under -transformatio…
Notes on flat pseudo-Riemannian manifolds
Fabricio Valencia
In these notes we survey basic concepts of affine geometry and their interaction with Riemannian geometry. We give a characterization of affine manifolds which has as counterpart t…
Flat affine symplectic Lie groups
Fabricio Valencia
We give a new characterization of flat affine manifolds in terms of an action of the Lie algebra of classical infinitesimal affine transformations on the bundle of linear frames. W…