The natural brackets on couples of vector fields and 1-forms

The natural brackets on couples of vector fields and 1-forms

All natural bilinear operators transforming pairs of couples of vector fields and 1-forms into couples of vectorfields and 1-forms are found. All natural bilinear operators as above satisfying the Leibniz rule are extracted. All naturalLie algebra brackets on couples of vector fields and 1-forms are collected.

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