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arXiv · 2308.10432

On Sasakian quasi-Killing spinors in three-dimensions

Satsuki Matsuno·Fumihiro Ueno
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Abstract

A Sasakian quasi-Killing spinor (SqK-spinor), which is a generalization of a Killing spinor on Sasakian manifolds, was defined in \cite{Kim Friedrich 2000}.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 motion of a charged particle in the presence of a contact Maxwell field can be depicted using an SqK-spinor. urthermore, 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.

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Satsuki Matsuno, Fumihiro Ueno. 2023-08-21. On Sasakian quasi-Killing spinors in three-dimensions. https://doi.org/10.7546/jgsp-72-2025-59-81

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