Th. Friedrich, Solutions of the Einstein-Dirac Equation on Riemannian Manifolds with Constant Scalar Curvature, math.DG/0002182, to appear in J. Geom. Phys. Home/Search Document Details and Download
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The Einstein-Dirac Equation On Sasakian 3-Manifolds - Belgun (2000) (Correct)
....p 5 2 , and is not a Killing spinor. The examples from (i) to (iii) are due to Th. Friedrich and E.C. Kim [4] The last 2 examples are part of a 1 parameter (modulo homothety) family of metrics on 3 manifolds with constant eigenvalues of the Ricci tensor, which, as shown by Th. Friedrich [3], are the only ones that admit non trivial Einstein spinors, and do not admit Killing spinors. The proof of the Theorem is divided in two steps: first (Section 3) we prove (using the WK equation (5) that, if the scalar curvature is non vanishing and the manifold admits locally an Einstein spinor, ....
Th. Friedrich, Solutions of the Einstein-Dirac Equation on Riemannian Manifolds with Constant Scalar Curvature, math.DG/0002182, to appear in J. Geom. Phys.
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