27 citations · 47 across the 6 of their papers we have counts for
4 papers · 1 filter
The super-Sasaki metric on the antitangent bundle
Andrew James Bruce
We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shi…
Connections Adapted to Non-Negatively Graded Structures
Andrew James Bruce
Graded bundles are a particularly nice class of graded manifolds and represent a natural generalisation of vector bundles. By exploiting the formalism of supermanifolds to describe…
Modular classes of Q-manifolds: a review and some applications
Andrew James Bruce
A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold -- which is viewed as the obstruction to the…
Introduction to graded bundles
Andrew J. Bruce, K. Grabowska, J. Grabowski
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hinds…