Submersive second order ordinary differential equations

Abstract

The objectives of this paper are to define and to characterize submersive second order ordinary differential equations (ODE) and to examine several situations in which such ODE occur. This definition and characterization is in terms of tangent bundle geometry as developed in [4, 6, 7, 10, 11, 14]. From this viewpoint second order ODE are identified with a special vector field on the tangent bundle. The ODE are said to be submersive when this vector field and the canonical vertical endomorphism [14] define a foliation, relative to which the vector field passes to the local quotient.