New Solutions of the Einstein-Dirac Equation in Dimension n=3
Abstract
The aim of this short note is to announce the existence of a one-parameter family of left-invariant metrics on S3 admitting WK-spinors. This family contains the two non-Einstein Sasakian metrics with WK-spinors on S3, but does not contain the standard sphere S3 with Killing spinors. Moreover, any simply-connected, complete Riemannian manifold X3 = S3 with WK-spinors such that the eigenvalues of the Ricci tensor are constant is isometric to a space of this one-parameter family.
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