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)⊕sℝn and in a space of constant curvature the Lie algebra is so(n). Furthermore, if the space has one section of constant curvature of dimensi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/532690 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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)⊕sℝn 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 n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n≥∑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). |
|---|---|
| ISSN: | 1110-757X 1687-0042 |