VB-structures and generalizations
2021
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 homogeneity structure. The latter is a smooth action of the monoid $(\mathbb{R},\cdot)$ of multiplicative reals on $F$. Vector bundles are particular cases of homogeneity structures and weighted structures on them we call VB-structures. In the case of Lie algebroids and Lie groupoids, weighted structures include the concepts of VB-algebroids and VB-groupoids, intensively studied recently in the literature. Investigating various weighted structures, we prove some interesting results about their properties.
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