132 citations · 1.9k across the 101 of their papers we have counts for
48 papers · 1 filter
Lifting statistical structures
Katarzyna Grabowska, Janusz Grabowski, Marek Kuś +1
We consider some natural (functorial) lifts of geometric objects associated with statistical manifolds (metric tensor, dual connections, skewness tensor, etc.) to higher tangent bu…
VB-structures and generalizations
Janusz Grabowski, Katarzyna Grabowska, Zohreh Ravanpak
Motivated by properties of higher tangent lifts of geometric structures, we introduce concepts of weighted structures for various geometric objects on a manifold F equipped with a…
Nonassociative analogs of Lie groupoids
Janusz Grabowski, Zohreh Ravanpak
We introduce nonassociative geometric objects generalising naturally Lie groupoids and called (smooth) quasiloopoids and loopoids. We prove that the tangent bundles of smooth loopo…
Information geometry on groupoids: the case of singular metrics
Katarzyna Grabowska, Janusz Grabowski, Marek Kus +1
We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defin…
Transitive nilpotent Lie algebras of vector fields and their Tanaka prolongations
Katarzyna Grabowska, Janusz Grabowski, Zohreh Ravanpak
Transitive local Lie algebras of vector fields can be easily constructed from dilations of associating with coordinates positive weights (give me a sequence of p…
Solvable Lie Algebras of Vector Fields and a Lie's Conjecture
Katarzyna Grabowska, Janusz Grabowski
We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's…