Constructing a Space from the System of Geodesic Equations
Differential Geometry
2009-11-13 v1 Classical Analysis and ODEs
Abstract
Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from the Christoffel symbols. The procedure is extended for determining if a second order quadratically semi-linear system can be expressed as a system of geodesic equations, provided it has terms only quadratic in the first derivative apart from the second derivative term. A computer code has been developed for dealing with larger systems of geodesic equations.
Cite
@article{arxiv.0711.1217,
title = {Constructing a Space from the System of Geodesic Equations},
author = {E. Fredericks and F. M. Mahomed and E. Momoniat and Asghar Qadir},
journal= {arXiv preprint arXiv:0711.1217},
year = {2009}
}