Reeb vector field

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 $\alpha$, the Reeb vector field satisfies ${\displaystyle R\in \mathrm {ker} \ d\alpha ,\ \alpha (R)=1}$,
• in particular, in the context of Sasakian manifold#The Reeb vector field.