A Note on Flat Metric Connections with Antisymmetric Torsion
نویسندگان
چکیده
In this short note we study flat metric connections with antisymmetric torsion T 6= 0. The result has been originally discovered by Cartan/Schouten in 1926 and we provide a new proof not depending on the classification of symmetric spaces. Any space of that type splits and the irreducible factors are compact simple Lie group or a special connection on S. The latter case is interesting from the viewpoint of G2-structures and we discuss its type in the sense of the Fernandez-Gray classification. Moreover, we investigate flat metric connections of vectorial type.
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