A note on flat metric connections with antisymmetric torsion

Details A note on flat metric connections with antisymmetric torsion A note on flat metric connections with antisymmetric torsion

2009-11-09

arxiv.org/abs/0911.1602v1

Mathematics

Differential Geometry

10 pages. to appear in Differ. Geom. Appl

Scientific paper

In this short note we study flat metric connections with antisymmetric torsion $T \neq 0$. 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.

Affiliated with

Also associated with

No associations

Rating

A note on flat metric connections with antisymmetric torsion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A note on flat metric connections with antisymmetric torsion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A note on flat metric connections with antisymmetric torsion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-659756