Copyright © 2012 Adnan Aslam and Asghar Qadir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an -area enclosing a constant -volume in a Euclidean space is and in a space of constant curvature the Lie algebra is . Furthermore, if the space has one section of constant curvature of dimension , another of , and so on to and one of zero curvature of dimension , with (as some of the sections may have no symmetry), then the Lie algebra of Noether symmetries is .