Generalized harmonic maps

  • Jürgen Jost
Part of the Lectures in Mathematics ETH Zürich book series (LM)


In § 1.3, we had introduced harmonic maps between Riemannian manifolds. For a map f: MN between Riemannian manifolds M, N, the energy was defined as
$$ {2}\,\int\limits_M {\left\| {df(x)} \right\|^2 d\mu (x)}$$
where dμ 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.


Riemannian Manifold Homotopy Class Finite Index Closed Geodesic Nonpositive Curvature 
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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