# Questions tagged [sasakian-geometry]

A Sasakian manifold is a contact manifold $(M,\theta)$ equipped with a special kind of Riemannian metric $g$, called a Sasakian metric.

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### Spin structures on Sasakian manifolds and the Kähler analogy

A Sasakian manifold is often said to be the odd dimensional analogue of a Kähler manifold.
Now for a $2n$-dimensional Kähler manifold we know from Atiyah that it is spin exactly if the line bundle $\...

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### Moduli space of null Sasaki $η$-Einstein structures for higher dimensions(Calabi-Yau structures in Sasakian setting)

The moduli space of null Sasaki $η$-Einstein structures for simply connected compact 5-dimensional manifold $M$ is determined by the following quadric
$$\{[\alpha]\in H^2(M,\mathbb C) \; \text{such ...

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### $S^3$ as a Sasakian Manifold

Reading about Sasakian manifolds one come across two slogans:
A) "A Sasakian manifold is an odd-dimensional analogue of a Kahler manifold."
B) "A Sasakian manifold sits between two Kahler manifolds -...

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### Quaternion-Sasakian manifolds and special holonomy Sasakian manifolds

Two well-known slogans are
A Sasakian manifold is the odd dimensional analogue of a Kähler manifold
and
A $3$-Sasakian manifold is the odd dimensional analogue of a hyper-Kähler manifold
Does this ...

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### Is every 3-Sasakian a Sasakian-Einstein manifold?

a short question: Is every 3-Sasakian manifold a Sasaki-Einstein manifold? If not, do you have an example? If yes, how can I prove this?
Thanks and best regards