A vector field $\vec{F} = \vec{F}(x,\,y,\,z)$ defined in an open set $D$ of $\mathbb{R}^3$ is lamellar if the condition $$\nabla\!\times\!\vec{F} = \vec{0}$$ is satisfied in every point $(x,\,y,\,z)$ , of $D$

Here, $\nabla\!\times\!\vec{F}$ is the curl or rotor of $\vec{F}$ The condition is equivalent with both of the following:

• The line integrals $$\oint_s \vec{F}\cdot d\vec{s}$$ 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 $$\vec{F} = \nabla u.$$

Note. In physics, $u$ is in general replaced with $V = -u$ If the $\vec{F}$ 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 $P_0$ to infinity.