Hi All, I am going over a definition of a Contact Vector Field defined on a 3-manifold: this is defined as " a vector field v whose flow preserves the contact structure " .(adsbygoogle = window.adsbygoogle || []).push({});

1) Background (sorry if this is too simple) A contact structure ## \xi ##( let's stick to 3-manifolds for now ) is a nowhere-integrable plane bundle on a 3-manifold M^3, i.e., we have a 2-plane distribution so that there are no submanifolds N < M^3 (i.e., surfaces here) so that TN = ## \xi ## , i.e., there are no submanifolds N of M^3 whose tangent bundle coincides with the contact distribution (this is related to one of Frobenius' theorems and involutivity).

Now ,does the statement " the flow of the vector field v preserves the contact structure" mean that the tangent space T_C(t) along any flow curve C(t) (local or global) coincides with the contact plane at C(t) ?

Thanks.

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# Contact Vector Fields. "Flow Preserves Contact Structure?

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