Differential Invariants of Second-Order Ordinary Differential Equations
The notion of a differential invariant for systems of second-order differential equations σ on a manifold M with respect to the group of vertical automorphisms of the projection p: ℝ ×M → ℝ, is defined and the Chern connection ∇ σ attached to a SODE σ allows one to determine a basis for second-order differential invariants of a SODE.
KeywordsVector Bundle Curvature Mapping Tensor Field Linear Connection Order Ordinary Differential Equation
Supported by Ministerio of Ciencia e Innovación of Spain (MICINN), under grant #MTM2008–01386.
- 5.Kumpera, A.: Invariants différentiels d’un pseudogroupe de Lie. I, II. J. Diff. Geom. 10, 289–345, 347–416 (1975)Google Scholar