132 citations · 1.9k across the 101 of their papers we have counts for
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Higher order mechanics on graded bundles
Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted al…
Linear duals of graded bundles and higher analogues of (Lie) algebroids
Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski
Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We pre…
-Supergeometry II: Batchelor-Gawedzki Theorem
Tiffany Covolo, Janusz Grabowski, Norbert Poncin
Quite a number of -gradings, , appear in Physics and in Mathematics. The corresponding sign rules are given by the `scalar product' of the involved $\mathb…
-Supergeometry I: Manifolds and Morphisms
Tiffany Covolo, Janusz Grabowski, Norbert Poncin
In Physics and in Mathematics -gradings, , do appear quite frequently. The corresponding sign rules are determined by the `scalar product' of the involved…
Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings
Katarzyna Grabowska, Janusz Grabowski, Pawel Urbanski
The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for po…