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


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.


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R. Langevin. Yu. Nikolayevsky. "Three viewpoints on the integral geometry of foliations." Illinois J. Math. 43 (2) 233 - 255, Summer 1999.


Published: Summer 1999
First available in Project Euclid: 19 October 2009

zbMATH: 1009.53054
MathSciNet: MR1703185
Digital Object Identifier: 10.1215/ijm/1255985212

Primary: 53C12
Secondary: 53C65

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 2 • Summer 1999
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