## Abstract

In § 1.3, we had introduced harmonic maps between Riemannian manifolds. For a map
where

*f*:*M*→*N*between Riemannian manifolds*M*,*N*, the energy was defined as$$
{2}\,\int\limits_M {\left\| {df(x)} \right\|^2 d\mu (x)}$$

*d*μ is the measure on*M*induced by the Riemannian metric,*df*is the differential of*f*, and the norm ‖ · ‖ is induced by the Riemannian metrics of*M*and*N*. Smooth minimizers, or more generally solutions of the associated Euler-Lagrange equations, were called harmonic maps.## Keywords

Riemannian Manifold Homotopy Class Finite Index Closed Geodesic Nonpositive Curvature
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Basel AG 1997