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Commuting of exterior derivative and contraction (vector-valued forms)
$\newcommand{\sig}{\sigma}$
$\newcommand{\tr}{\operatorname{tr}_{\eta}}$
$\newcommand{\al}{\alpha}$
$\newcommand{\be}{\beta}$
$\newcommand{\til}{\tilde}$
Let $E$ be a smooth vector bundle over a ...
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