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.

Filter by
Sorted by
Tagged with
1
vote
1answer
115 views

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 ...
2
votes
1answer
148 views

$S^3$ 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 -...
12
votes
1answer
307 views

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 $\...
0
votes
1answer
239 views

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
3
votes
0answers
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 ...