A vector field F = F(x, y, z), defined in an open set D of ℝ³, is lamellar if the condition

is satisfied in every point (x, y, z) of D.

Here, ∇×F is the curl or rotor of F. The condition is equivalent with both of the following:

• The line integrals
  

  taken around any closed contractible curve s vanish.

• The vector field has a scalar potential u = u(x, y, z) which has continuous partial derivatives and which is up to a constant term unique in a simply connected domain; the scalar potential means that
  

The scalar potential has the expression

where the point P₀ may be chosen freely, P = (x, y, z).

Note. In physics, u is in general replaced with V = −u. If the F is interpreted as a force, then the potential V is equal to the work made by the force when its point of application is displaced from P₀ to infinity.