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Jacobi fields and linear connections for arbitrary second-order ODEs |
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| Authors: | M. Jerie G. E. Prince |
| Affiliation: | a Department of Mathematics, La Trobe University, Vic. 3086, Australia b School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia |
| Abstract: | We discuss generalisations of Jacobi fields and Raychaudhuri’s equation from the geodesic case to that of an arbitrary system of second-order ODEs. Our results are obtained using a natural choice of linear connection on evolution space. |
| Keywords: | Jacobi tensors Raychaudhuri’s equation Singularity analysis Congruence collapse Second-order differential equation |
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