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.
8
questions
12
votes
1
answer
383
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 $\...
4
votes
0
answers
142
views
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 ...
3
votes
2
answers
674
views
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.
3
votes
0
answers
131
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 ...
2
votes
1
answer
195
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 -...
2
votes
0
answers
72
views
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, ...
1
vote
1
answer
136
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 ...
0
votes
1
answer
281
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