Artículos de revistas
A Berger-type theorem for metric connections with skew-symmetric torsion
Fecha
2012-12Registro en:
Reggiani, Silvio Nicolás; A Berger-type theorem for metric connections with skew-symmetric torsion; Elsevier Science; Journal Of Geometry And Physics; 65; 12-2012; 26-34
0393-0440
CONICET Digital
CONICET
Autor
Reggiani, Silvio Nicolás
Resumen
We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere, then the space must be locally isometric to a Lie group with a bi-invariant metric or its symmetric dual (we assume the space to be locally irreducible). We also prove that a (simple) Lie group with a bi-invariant metric admits only two flat metric connections with skew-symmetric torsion: the two flat canonical connections. In particular, we get a refinement of a well-known theorem of Cartan and Schouten. Finally, we show that the holonomy group of a metric connection with skew-symmetric torsion on these spaces generically coincides with the Riemannian holonomy.