Legendre foliations on contact manifolds
| Autor: | Paulette Libermann |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Pure mathematics
Integrable system Legendre (foliation and transformation) Mathematical analysis Contact (forms and structures) Manifold Associated Legendre polynomials Computational Theory and Mathematics Jacobi structure Foliation (geology) Mathematics::Differential Geometry Geometry and Topology Affine transformation Invariant (mathematics) Poincaré-Cartan integral invariant “pseudo-orthogonal” distribution Mathematics::Symplectic Geometry Legendre polynomials Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 1:57-76 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/0926-2245(91)90022-2 |
| Popis: | Using Jacobi structures methods, we investigate properties of Legendre foliations on contact manifolds. We show that a Legendre foliation F on a contact manifold is “complete” if and only if the “pseudo-orthogonal” distribution F ⊥ is completely integrable; then the leaves of F and F ⊥ have affine structures. We show that for any Legendre foliation, the contact form is locally equivalent to the Poincare-Cartain integral invariant σpidxiHdt; we study the special cases a) H is a constant (complete case), b) (∂2H/∂pi∂pj) is non-degenerate. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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