Is there a classification of Sasaki or Sasaki-Einstein manifolds? What are important examples?
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$\begingroup$ "important" is one of those words which is probably observer-dependent. So what do you have in mind by an important example? i.e., important for what? I could perhaps add some more to my answer in order to address that question. $\endgroup$– José Figueroa-O'FarrillCommented Nov 16, 2010 at 23:19
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The book Sasakian Geometry by Charles Boyer and the late Krzysztof Galicki contains a wealth of information on this topic. As far as I know there is no classification, but there are of course tons of examples.
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$\begingroup$ I am for example interessting what is the Reeb vectorfield $\xi$ and the Sasaki structure $\Phi$ in special examples, may be in $M=S^{2m+1}$ or $M=\mathbb{R}^{2m+1}$. Can you say this? Thank you and best regards $\endgroup$ Commented Nov 19, 2010 at 13:55