The linearized system for isometric embeddings and its characteristic variety (Q411733)

Starting with the classical problem of finding an isometric embedding for an \(n\)-dimensional Riemannian manifold the authors introduce a smaller yet equivalent linearized system of equations. This equivalent linearized system is then put in an explicit form by introducing appropriate parameters. Based on this explicit expression, it is proved that the characteristic variety is not smooth for all higher dimensions when these parameters are sufficiently small. On this way, a conjecture of Bryant, Griffiths and Yang is proved.