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

Pawel Nurowski; George A J Sparling

doi:10.1088/0264-9381/20/23/004

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arXiv · math/0306331

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

Pawel Nurowski·George A J Sparling

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Abstract

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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BibTeX RIS

Pawel Nurowski, George A J Sparling. 2003-09-24. 3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations. https://doi.org/10.1088/0264-9381%2F20%2F23%2F004

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