Laguerre form

In mathematics, the Laguerre form is a tensor-valued form on an embeded surface, whose ratio with the infinitesimal line element cubed is invariant with respect to a choice of frame.

Definition

This defintion comes from Cartan, translated into more modern notation.
Consider some surface embedded in a three dimensional Riemannian manifold. On, define an orthonormal coframe, and let be the second fundamental form, and the exterior covariant derivative. The Laguerre form is a tensor-valued form defined byor using Einstein summation notation,