Complete lifting of double-linear semi-basic tangent valued forms to Weil like functors on double vector bundles

Abstract

. Let F be a product preserving gauge bundle functor on double vector bundles. We introduce the complete lifting F ϕ : FK → ∧ p T ∗ FM ⊗ TFK of a double-linear semi-basic tangent valued p -form ϕ : K → ∧ p T ∗ M ⊗ TK on a double vector bundle K with base M . We prove that this com- plete lifting preserves the Frolicher–Nijenhuis bracket. We apply the results obtained to double-linear connections.