3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

Details 3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations 3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

2003-06-23

arxiv.org/abs/math/0306331v3

Mathematics

Differential Geometry

Scientific paper

10.1088/0264-9381/20/23/004

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

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