# 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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### Calabi–Yau theorem and complex Monge–Ampère equation for transversally Kähler manifolds

Let $M$ be a compact smooth manifold, and $F\subset TM$ a smooth foliation. It is called transversally Kähler if the normal bundle $TM/F$ is equipped with a Hermitian structure (that is, a complex ...
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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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### $S^3$ 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 -...
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 $\... 3 votes 0 answers 127 views ### Moduli space of null Sasaki$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 ... 