[ Home ] [ About Us ] [ Research ] [ People ] [ Publications ] [ News ] [ Other Info ] [ Impressum ]
Sfb288 logo Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 586


On the holonomy of connections with skew-symmetric torsion

Ilka Agricola and Thomas Friedrich

We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated $2$-form or any spinor. Suitable integral formulas allow us to prove similar properties in case of a compact Riemannian manifold equipped with a metric connection of skew-symmetric torsion. On the Aloff-Wallach space $N(1,1)$ we construct families of connections admitting parallel spinors. Furthermore, we investigate the geometry of these connections as well as the geometry of the underlying Riemannian metric. Finally, we prove that any $7$-dimensional $3$-Sasakian manifold admits $mathbb{P}^2$-parameter families of linear metric connections and spinorial connections defined by $4$-forms with parallel spinors.


No PostScript version available.


Copyright © 1999 Sfb 288, Mathematics 8-5, Strasse des 17 Juni 136, TU-Berlin, 10623 Berlin
[ Home ] [ About Us ] [ Research ] [ People ] [ Publications ] [ News ] [ Other Info ] [ Impressum ]