Explore relationships

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 α{\displaystyle \alpha }, the Reeb vector field satisfies R∈kerdα,α(R)=1{\displaystyle R\in \mathrm {ker} \ d\alpha ,\ \alpha (R)=1},in particular, in the context of Sasakian manifold.If a contact manifold arises as a constant-energy hypersurface inside a symplectic manifold, then the Reeb vector field is the restriction to the submanifold of the Hamiltonian vector field associated to the energy function.

Use + to expand a branch. Click a topic name to open its summary.