After 1970—Genuine Generalizations
In the preceding chapter, we described work that uses or generalizes Noether’s second theorem. Now we shall look at the generalizations of her first theorem that began to appear in the 1970s. After the pioneering work of Trautman , geometric studies of that theorem began to be undertaken. The first such studies consisted of finding an invariant formulation of the first theorem in the framework of the geometry of differentiable manifolds, which is to say, without using local coordinates. This was accomplished for first-order Lagrangians by Goldschmidt and Sternberg . As was observed above, the passage to a greater number of independent variables and to higher-order Lagrangians was accomplished in papers that are too numerous to be listed here.
KeywordsGeneralize Vector Generalize Symmetry Base Manifold Differentiable Manifold Soliton Equation
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