0000000000617563

AUTHOR

R. Langevin

showing 2 related works from this author

Feuilletages deCP(n) : de l’holonomie hyperbolique pour les minimaux exceptionnels

1992

Let ℱ be a holomorphic foliation ofCP(n). If ℱ has a leaf L, the closure L of which is disjoint from the singular set of the foliation, we prove that there exists a loop in a leaf contained in L with contracting hyperbolic holonomy.

Mathematics::Dynamical SystemsQuantitative Biology::Tissues and OrgansGeneral MathematicsMathematical analysisHolomorphic functionHolonomyClosure (topology)Disjoint setsFoliationCombinatoricsLoop (topology)Mathematics::Differential GeometryMathematics::Symplectic GeometryMathematicsPublications mathématiques de l'IHÉS
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Three viewpoints on the integral geometry of foliations

1999

We deal with three different problems of the multidimensional integral geometry of foliations. First, we establish asymptotic formulas for integrals of powers of curvature of foliations obtained by intersecting a foliation by affine planes. Then we prove an integral formula for surfaces of contact of an affine hyperplane with a foliation. Finally, we obtain a conformally invariant integral-geometric formula for a foliation in three-dimensional space.

Convex geometryMathematics::Dynamical SystemsGeneral MathematicsMathematical analysisAbsolute geometryGeometry53C65Viewpoints53C12Integral geometryOrdered geometryMathematics::Differential GeometryConformal geometryMathematics::Symplectic GeometryMathematics
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