Infinitesimal Deformations of Complete Vector Fields are Complete

@inproceedings{Kock1986InfinitesimalDO,
  title={Infinitesimal Deformations of Complete Vector Fields are Complete},
  author={Anders Kock},
  year={1986}
}
Recall that a vector field X on a smooth manifold M is complete if it generates a global flow ξ : M × R → M . If Xǫ is a smoothly parametrized family of vector fields (ǫ ∈ R), it may happen that X0 is complete but all Xǫ with ǫ 6= 0 are incomplete. This is the case for instance with the family of vector fields ǫ · x · ∂ ∂x on R. We shall prove, however, that in the context of synthetic differential geometry, if X0 is complete, then so is Xǫ for any ǫ with ǫ 2 = 0. We presuppose some general… CONTINUE READING

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