A note on flat metric connections with antisymmetric torsion

作者：Agricola Ilka^*; Friedrich Thomas

来源：Differential Geometry and its Applications, 2010, 28(4): 480-487.

DOI：10.1016/j.difgeo.2010.01.004

• Flat connections
• Skew-symmetric torsion

In this short note we study flat metric connections with antisymmetric torsion T not equal 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(7). The latter case is interesting from the viewpoint of G(2)-structures and we discuss its type in the sense of the Fernandez-Gray classification. Moreover, we investigate flat metric connections of vectorial type.

• 出版日期2010-8