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On Eta-Einstein Sasakian Geometry

Charles P. Boyer·Krzysztof Galicki·Paola Matzeu
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Abstract

We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl structures.

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Charles P. Boyer, Krzysztof Galicki, Paola Matzeu. 2005-10-31. On Eta-Einstein Sasakian Geometry. https://doi.org/10.1007/s00220-005-1459-6

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