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1.2.3
Soit ℱ \mathscr{F} forme
de type ( p , q ) (p,q) ℱ \mathscr{F} U U est un
élément de
ℱ V p , q ( U ) := ℱ V ( U ) ⊗ 𝒜 V ( U ) 𝒜 V p , q ( U ) = ℱ ( U ) ⊗ 𝐑 Λ p V → ∗ ⊗ 𝐑 Λ q V → ∗ . \mathscr{F}_{V}^{p,q}(U):=\mathscr{F}_{V}(U)\otimes_{\mathscr{A}_{V}(U)}\mathscr{A}_{V}^{p,q}(U)=\mathscr{F}(U)\otimes_{\mathbf{R}}\Lambda^{p}\overrightarrow{V}^{*}\otimes_{\mathbf{R}}\Lambda^{q}\overrightarrow{V}^{*}.