Geodesic
Minimal, rigid foliations by curves on $\mathbb{CP}^n$
Journal of the European Mathematical Society, Tome 5 (2003) no. 2, pp. 147-201 Cet article a éte moissonné depuis la source EMS Press

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We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space CPn for every dimension n≥2 and every degree d≥2. Precisely, we construct a foliation F which is induced by a homogeneous vector field of degree d, has a finite singular set and all the regular leaves are dense in the whole of CPn. Moreover, F satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if F is conjugate to another holomorphic foliation by a homeomorphism sufficiently close to the identity, then these foliations are also conjugate by a projective transformation. Finally, all these properties are persistent for small perturbations of F.
DOI : 10.1007/s10097-002-0049-6
Classification : 14-XX, 00-XX
Keywords: 
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     author = {Frank Loray and Julio C. Rebelo},
     title = {Minimal, rigid foliations by curves on $\mathbb{CP}^n$},
     journal = {Journal of the European Mathematical Society},
     pages = {147--201},
     year = {2003},
     volume = {5},
     number = {2},
     doi = {10.1007/s10097-002-0049-6},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10097-002-0049-6/}
}
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Frank Loray; Julio C. Rebelo. Minimal, rigid foliations by curves on $\mathbb{CP}^n$. Journal of the European Mathematical Society, Tome 5 (2003) no. 2, pp. 147-201. doi: 10.1007/s10097-002-0049-6

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