Three-dimensional Cauchy–Riemann structures and second-order ordinary differential equations

Abstract

The equivalence problem for second order ODEs given modulo point\ntransformations is solved in full analogy with the equivalence problem of\nnondegenerate 3-dimensional CR structures. This approach enables an analog of\nthe Feffereman metrics to be defined. The conformal class of these (split\nsignature) metrics is well defined by each point equivalence class of second\norder ODEs. Its conformal curvature is interpreted in terms of the basic point\ninvariants of the corresponding class of ODEs.\n