# Tag Info

### Kähler metric with two compatible complex structures

No, you cannot prove this because it is not true. For example, consider $M$ to be the product of two oriented, complete Riemannian surfaces $M=\Sigma_1\times\Sigma_2$ where $g$ is the product metric ...
• 103k
Accepted

### Do these definitions of integrable quaternionic structure agree?

These two 'definitions' do not agree. Also, you should be careful about your choice of sources. Most differential geometers use the terminology 'almost quaternionic' to mean that the structure group ...
• 103k
Accepted

• 875
1 vote
Accepted

### Can deformation equivalent Kähler manifolds always be obtained by a deformation where all the fibers are Kähler?

I don't think this is known. For hyperkahler manifolds, conjecturally, all smooth complex deformations are class C and birational to hyperkahler. If this is true, your conjecture would follow ...
• 8,828
1 vote
Accepted

### Stuck on a computation with quaternions and moment maps

I was able to finally prove that $$d(\omega.d\mathbf{r}) = - \frac{1}{2r^3}(d\mathbf{r}\,\mathbf{r} \wedge d\mathbf{r}).$$ In the process, I have learned a lot. The main issue for me was that I was ...
• 4,103
1 vote

### The state of art of the singular Levi problem -- and hyperkähler quotients

Privet, Anya. Your reference [FN80] actually seems to contain an answer to this problem! They state (in particular, see the question 1.5 in the introduction) that the class of weakly psh functions, i....
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