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In this short note we study flat metric connections with antisymmetrictorsion $T \neq 0$. The result has been originally discovered byCartan/Schouten in 1926 and we provide a new proof not depending on theclassification of symmetric spaces. Any space of that type splits and theirreducible factors are compact simple Lie group or a special connection on$S^7$. The latter case is interesting from the viewpoint of $G_2$-structuresand we discuss its type in the sense of the Fernandez-Gray classification.Moreover, we investigate flat metric connections of vectorial type.

A note on flat metric connections with antisymmetric torsion