Integrals of foliations on manifolds with a generalized symplectic structure

Ronald Owen Fulp and Joe Alton Marlin

Vol. 67 (1976), No. 2, 373–387

DOI: 10.2140/pjm.1976.67.373

Abstract

Let M be a C^∞ manifold of dimension m and E an integrable subbundle (foliation) of the tangent bundle TM. We are interested in structures on the set of all local integrals of E. For example, if M is a symplectic manifold then the Poisson brackets operation on the set C_loc^∞ of all local functions of M defines an algebraic structure on C_loc^∞. Earlier authors have called such structures “function groups.” In particular, if X_H is a nonvanishing Hamiltonian vector field, then X_H defines a foliation E of M and the set of all local integrals of E is also a function group.

Mathematical Subject Classification

Primary: 57D30, 57D30

Secondary: 57D25

Milestones

Received: 11 December 1975

Revised: 6 July 1976

Published: 1 December 1976