Reeb vector field
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:
Vector field
In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...
, named after the French mathematician Georges Reeb
Georges Reeb
Georges Henri Reeb was a French mathematician. He worked in differential topology, differential geometry, differential equations, topological dynamical systems theory and non-standard analysis....
, is a notion that appears in various domains of contact geometry
Contact geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle and specified by a one-form, both of which satisfy a 'maximum non-degeneracy' condition called 'complete non-integrability'...
including:
- in a contact manifold, given a contact 1-form
, the Reeb vector field satisfies 
, - in particular, in the context of Sasakian manifold#The Reeb vector field.