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Reeb vector field

From Wikipedia, the free encyclopedia

In mathematics, the Reeb vector field, named after the French mathematician Georges Reeb, is a notion that appears in various domains of contact geometry including:

  • in a contact manifold, given a contact 1-form , the Reeb vector field satisfies ,[1][2]
  • in particular, in the context of Sasakian manifold.

Definition

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Let be a contact vector field on a manifold of dimension . Let for a 1-form on such that . Given a contact form , there exists a unique field (the Reeb vector field) on such that:[3]

.

See also

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References

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  1. ^ John B. Etnyre. "Contact manifolds" (PDF). Archived from the original (PDF) on 2018-04-04.
  2. ^ "Contact structures and Reeb vector fields" (PDF). Archived from the original (PDF) on 2016-05-09.
  3. ^ C. Vizman, "Some Remarks on the Quantomorphism Group" (1997)