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

Authors: MIROSLAV DOUPOVEC, JAN KUREK, WLODZIMIERZ MIKULSKI

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

Keywords: Natural operator, vector field, $1$-form, Leibniz rule

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