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5 votes
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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 ...
Ali Taghavi's user avatar
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 ...
Darius Alexander's user avatar
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 ...
Carlos Martinez's user avatar
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 $\partial M$ ...
Eugene Rabinovich's user avatar