A p-brane Newton-Cartan structure admits a torsion-free compatible affine connection exactly when it is Augustinian, and all such connections are classified by longitudinal-frame field strengths.
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p-brane Newton--Cartan Geometry
A p-brane Newton-Cartan structure admits a torsion-free compatible affine connection exactly when it is Augustinian, and all such connections are classified by longitudinal-frame field strengths.