Abstract.
In this note, we find the conditions on an odd-dimensional Riemannian manifolds under which its twistor space is eta-Einstein. This can be used to yield an Einstein metric on the tangent sphere bundle of any 3-dimensional manifold of positive constant curvature.
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Davidov, J. Eta-Einstein condition on twistor spaces of odd-dimensional Riemannian manifolds. J. geom. 86, 42–53 (2007). https://doi.org/10.1007/s00022-006-0050-4
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DOI: https://doi.org/10.1007/s00022-006-0050-4