Linear natural liftings of forms to Weil bundles with Weil algebras

doi:10.1285/i15900932v28n2p99

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

Jacek D¸ebecki

Abstract

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 $q=0$ .