The asymptotic pseudoconformal structure on a four-dimensional hypersurface and its totally isotropic two-dimensional submanifolds (Q2366391)

A smooth hypersurface \(V^ n\) of the real projective space \(\mathbb{R} P^{n+1}\) defines, through the structural equations of an adapted moving frame, some quadratic form \(\Phi\), which is required to be non-degenerate here. The pseudoconformal structure induced by \(\Phi\) on \(V^ n\) is studied. In particular, for \(n=4\) the conformal curvature splits into selfdual and anti-selfdual parts, and \(V^ 4\) is in a sense generated by a family of isotropic surfaces \(V^ 2(\lambda)\).