Linear natural liftings of forms to Weil bundles with Weil algebras ${\mathbb D}^r_k$

Details Linear natural liftings of forms to Weil bundles with Weil algebras ${\mathbb D}^r_k$ Linear natural liftings of forms to Weil bundles with Weil algebras ${\mathbb D}^r_k$

2009-06-08

arxiv.org/abs/0906.1514v1

Mathematics

Differential Geometry

7 pages

Scientific paper

We give an explicit description and calculate the dimension of the vector space of linear natural liftings of $p$-forms on $n$-dimensional manifolds $M$ to $q$-forms on $T^{{\mathbb D}^r_k}M$, where ${\mathbb D}^r_k$ is the Weil algebra of $r$-jets at 0 of smooth functions ${\mathbb R}^k\longrightarrow{\mathbb R}$, for all non-negative integers $n$, $p$, $q$, $r$, $k$ except the case $p=n$ and $q=0$.

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