Noether Symmetries of the Area-Minimizing Lagrangian

Abstract

It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an(n-1)-area enclosing a constantn-volume in a Euclidean space isso(n)⊕sℝnand in a space of constant curvature the Lie algebra isso(n). Furthermore, if the space has one section of constant curvature of dimensionn1, another ofn2, and so on tonkand one of zero curvature of dimensionm, withn≥∑j=1knj+m(as some of the sections may have no symmetry), then the Lie algebra of Noether symmetries is⊕j=1kso(nj+1)⊕(so(m)⊕sℝm).