On Sasakian quasi-Killing spinors in three-dimensions
Satsuki Matsuno, Fumihiro Ueno
Mathematics, Differential Geometry, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th)
A Sasakian quasi-Killing spinor (SqK-spinor), which is a generalization of a Killing spinor on Sasakian manifolds, was defined by Kim and Friedrich. The purpose of this paper is to study in detail SqK-spinors on three-dimensional pseudo-Riemannian Sasakian space-form. We briefly review some results on SqK-spinors and then investigate some geometric properties. First, we demonstrate that the Reeb vector field is described by a specific SqK-spinor. Then we establish that the movement of charged particles in the presence of a contact Maxwell field can be depicted using an SqK-spinor. Furthermore, we find that almost all SqK-spinors provide solutions to the Einstein-Dirac system with a non-zero cosmological constant. Additionally, we reveal that a particular SqK-spinor in conjunction with a contact Maxwell field satisfies the Einstein-Dirac-Maxwell systems. Finally, we show explicit formulae of SqK-spinors in terms of elementary functions with respect to a certain frame.