6533b834fe1ef96bd129cdd7

RESEARCH PRODUCT

Three viewpoints on the integral geometry of foliations

R. LangevinYu. Nikolayevsky

subject

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

description

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.

yearjournalcountryeditionlanguage
1999-06-01
http://projecteuclid.org/euclid.ijm/1255985212