Abstract for Sfb Preprint No. 589

Killing spinors in Supergravity with 4-fluxes Ilka Agricola and Thomas Friedrich We study the spinorial Killing equation of supergravity involving a torsion $3$-form $\T$ as well as a flux $4$-form $\F$. In dimension seven, we construct explicit families of compact solutions out of $3$-Sasakian geometries, nearly parallel $\G_2$-geometries and on the homogeneous Aloff-Wallach space. The constraint $\F \cdot \Psi = 0$ defines a non empty subfamily of solutions. We investigate the constraint $\T \cdot \Psi = 0$, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically.