Projective invariants of planar 2-webs
The author investigates planar linear 2-webs and their projective differential invariants. By studying a certain representation of the Lie algebra \(\mathfrak{sl}_3(\mathbb{R})\) by vector fields she obtains that such an invariant is generated by two invariants \(J_1\) and \(J_2\), of order 2 and 3, respectively, and their invariant derivations. Furthermore, the field of these invariants separates regular \(\mathrm{SL}_3(\mathbb{R})\)-orbits. This then allows the author to characterize when two regular linear 2-webs are equivalent under the group \(\mathrm{SL}_3(\mathbb{R})\).
scientific article; zbMATH DE number 6955636