Solutions of the Einstein-Dirac Equation on Riemannian 3-Manifolds with Constant Scalar Curvature

TL;DR

This paper classifies all 3-dimensional manifolds with non-zero constant scalar curvature that admit non-trivial solutions to the Einstein-Dirac equation, advancing understanding of geometric structures compatible with spinor fields.

Contribution

It provides a complete classification of such manifolds, identifying the geometric conditions under which solutions exist.

Findings

Classification of manifolds with constant scalar curvature admitting solutions

Identification of geometric structures compatible with Einstein-Dirac solutions

Extension of known solutions to a broader class of 3-manifolds

Abstract

This paper contains a classification of all 3-dimensional manifolds with constant scalar curvature $S \not= 0$ that carry a non-trivial solution of the Einstein-Dirac equation.