Noether symmetries of the area-minimizing lagrangian

It is shown that the lie algebra of noether symmetries for the lagrangian minimizing an (n - 1) -area enclosing a constant n -volume in a euclidean space is so(n)⊕ s ℝ n and in a space of constant curvature the lie algebra is so (n). furthermore,if the space has one section of constant curvature of dimension n 1,another of n 2,and so on to n k and one of zero curvature of dimension m,with n ≥ σ j=1 k n j + m (as some of the sections may have no symmetry),then the lie algebra of noether symmetries is ⊕ j=1 k so(n j + 1) ⊕ (so (m)⊕ sℝ m). © 2012 adnan aslam and asghar qadir.