VB-structures and generalizations

Motivated by properties of higher tangent lifts geometric structures, we introduce concepts weighted structures for various objects on a manifold F equipped with homogeneity structure. The latter is smooth action the monoid $$(\mathbb {R},\cdot )$$ multiplicative reals. Vector bundles are particular cases and them call $$\mathrm{V\!B}$$ -structures. In case Lie algebroids groupoids, include -algebroids -groupoids, intensively studied recently in literature. Investigating prove some interesting results about their properties.