All Questions
10 questions
12
votes
3
answers
1k
views
Foliations by holomorphic curves on complex surfaces
On a complex surface, does there exist a non-singular foliation by holomorphic curves that is NOT a holomorphic foliation, i.e. a transversally holomorphic foliation?
The surface should be compact ...
- 2,858
3
votes
1
answer
205
views
Looking for examples of non-singular holomorphic foliations with compact leaves
I am looking for examples (or what is known about) of the following kind of object:
X compact Kähler manifold
F a non-singular holomorphic foliation on X (so given by a holomorphic subbundle of the ...
- 8,828
3
votes
1
answer
192
views
Holonomy of foliation with trivial normal bundle
I am wondering about the following situation. Suppose $X$ is a compact Kahler manifold and $F \subset T_X$ is a holomorphic foliation. Suppose that the ``normal bundle'' $T_X / F$ of the foliation is ...
- 1,908
3
votes
0
answers
85
views
Can a punctured ball $(B\setminus\{0\})\subset\mathbb{C}^n$ be foliated by complete leaves?
Recently Antonio Alarcón proved that in the case of the unit ball $B\subset\mathbb{C}^n$ for $n\geq 2$ every smooth closed complex submanifold of dimension $q\leq n$, $V\subset\mathbb{C}^n$ defines a ...
- 6,367
2
votes
1
answer
276
views
Complex fibration over complex torus
Let $M$ be a 3-dimensional complex manifold, and $\Lambda$ a discrete lattice in $\mathbb C^2$. Suppose there is a holomorphic submersion $f:M\to\mathbb{C}^2/\Lambda$ with fibers given by 1-...
- 28.9k
2
votes
0
answers
85
views
Holomorphic Foliations of 3-manifolds with boundary
Let $M$ be a 3-manifold $M$ with boundary $\partial M$, and endow $\partial M$ with the structure of a Riemann surface. Does there exist a foliation of $M$ by Riemann surfaces such that $\partial M$ ...
5
votes
0
answers
215
views
Singular foliations of $\mathbb{C}P^2$ that are compatible to Fubini-Study metric
Is there a complete classification of quadratic polynomial vector fields on $\mathbb{C}^2$ whose corresponding singular foliation of $\mathbb{C}P^2$ satisfies the property quoted below?
The regular ...
- 356
16
votes
3
answers
3k
views
References for holomorphic foliations
I'm looking for an introduction to holomorphic foliations and foliations of complex manifolds.
Any little helps, but I'm particularily interested in problems of the type where we have a hermitian ...
- 356
4
votes
0
answers
215
views
Kähler Cones in $\mathbb{C}^4$ and a foliation of $\mathbb{P}^3$
Take the 3-dimensional complex projective space $\mathbb{P}^3$. Consider the action of the group $SU(2)\times SU(2)$. I have read in physics related articles that these group gives a singular ...
- 101
3
votes
1
answer
345
views
extended forms from foliations [closed]
hi,
i have the following question: Let $M$ be a n-dimensional manifold (or riemannian or everything thats nice ...) and let $\mathcal{F}$ be a foliation of $M$ by surfaces. Assume, furthermore, that ...
- 14.4k