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## Main Question or Discussion Point

In the definition of F-related vector fields, F must be a diffeomorphism. Why must it be a diffeomorphism? What if F is smooth and bijective, but not a diffeo?

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In the definition of F-related vector fields, F must be a diffeomorphism. Why must it be a diffeomorphism? What if F is smooth and bijective, but not a diffeo?

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If you post the definition I might be able to help. I left my manifolds book at school.

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quasar987

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Suppose F: M-->N is a diffeomorphism. For every Y in TM (tangent bundle to M), there is a unique smooth vector field on N that is F-related to Y.If you post the definition I might be able to help. I left my manifolds book at school.

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Yes, I understand the smooth and bijective part, but what about the non-diffeo part?

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quasar987

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Then I hinted to the fact that your book defines the notion when F is diffeo probably because in that case, we are in the nice situation where to every vector field on N there exists a unique F-related vector field on M... which is probably the property that the authors needed.

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