The structure of Legendre foliations

Author:
Myung-Yull Pang

Journal:
Trans. Amer. Math. Soc. **320** (1990), 417-455

MSC:
Primary 58F18; Secondary 57R30, 58F05

DOI:
https://doi.org/10.1090/S0002-9947-1990-1016808-6

MathSciNet review:
1016808

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Abstract: The local and global structure of Legendre foliations of contact manifolds is analysed. The main invariant of a Legendre foliation is shown to be a quadratic form on the tangent bundle to the foliation--the fundamental quadratic form. The equivalence problem is solved in the case when the fundamental quadratic form is nondegenerate and a generalization of Chern's solution to the equivalence problem for Finsler manifolds is obtained. A normal form for Legendre foliations is given which is closely related to Weinstein's structure theorem for Lagrangian foliations. It is shown that every compact, simply connected leaf of a Legendre foliation is diffeomorphic to a sphere.

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DOI:
https://doi.org/10.1090/S0002-9947-1990-1016808-6

Article copyright:
© Copyright 1990
American Mathematical Society