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A question on generalized Einstein metrics on four-dimensional manifolds

I don't really know about any previous literature on the topic. But here is an example of a metric that satisfies the condition above but is not Einstein (in sloppy notation, but I hope it's clear any …
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3 votes

Kahler-Einstein metrics on Toric manifolds are Torus-invariant?

I would put this in the comments if I could. I think you will find the answer to your question here (I cannot access this paper): Y. Matsushima: Sur la structure de groupe d'homeomorphismes analytiq …
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