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Generalized harmonic maps

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

Abstract

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.

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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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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