Vol. 67, No. 2, 1976

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Integrals of foliations on manifolds with a generalized symplectic structure

Ronald Owen Fulp and Joe Alton Marlin

Vol. 67 (1976), No. 2, 373–387

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 Cloc of all local functions of M defines an algebraic structure on Cloc. Earlier authors have called such structures “function groups.” In particular, if XH is a nonvanishing Hamiltonian vector field, then XH 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
Received: 11 December 1975
Revised: 6 July 1976
Published: 1 December 1976
Ronald Owen Fulp
Joe Alton Marlin