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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3-Sasakian manifolds and contact Fano Kähler-Einstein manifolds

Let $(M,g)$ be a Riemannian manifold. The Riemannian cone of $M$ is $C(M) = M \times {\Bbb R}^{>0}$ with the metric $t^2 g + dt\otimes dt$. A manifold is called Sasakian if its cone is Kähler, ...
Misha Verbitsky's user avatar
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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 ...
Misha Verbitsky's user avatar
1 vote
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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 ...
Dick Johnson's user avatar
2 votes
1 answer
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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 -...
Fofi Konstantopoulou's user avatar
12 votes
1 answer
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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 $\...
Alesandro Levi's user avatar
3 votes
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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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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
user7028's user avatar
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Paper about Sasaki-Einstein manifolds

can you give me a good paper (in the sense of a simple introduction) about Sasaki-Einstein manifolds? Thank you and best regards Florian M.
Differentialgeometer's user avatar