First integrals and symmetries associated to invariant tensors and applications to lax-like vector fields

Summary

The techniques followed in previous papers are applied to vector fields X with a set of related tensor fields invariant under X. The techniques are potentially able to provide first integrals and new symmetry vectors of X. A geometric base underlying recent results on Lax-like differential equations is given and it is shown that any vector field X possesses local Lax-like associated differential equations.