By E. Noether’s famous theorem, if an integral in the calculus of variations has continuous one-parameter groups of symmetries, then a conservation law, or a first integral of the Euler-Lagrange equation for the integral, must be associated to each of such symmetries. A concrete stress-energy tensor for smooth maps has been found by P. Baird and J. Eells, who also explained its applications in the theory of harmonic maps [B-E]. This chapter is devoted to the relevant topics.
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