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Is there any classification of Sasaki oder Sasaki-Einstein manifolds? What are important examples?

Thank you and best regards Differentialgeometer

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"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. – José Figueroa-O'Farrill Nov 16 '10 at 23:19
up vote 4 down vote accepted

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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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 – Differentialgeometer Nov 19 '10 at 13:55

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