Abstract
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.
Citation
R. Langevin. Yu. Nikolayevsky. "Three viewpoints on the integral geometry of foliations." Illinois J. Math. 43 (2) 233 - 255, Summer 1999. https://doi.org/10.1215/ijm/1255985212
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