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topology > algebraic topology > manifold > differentiable manifold > harmonic map

geometry > topological space > manifold > differentiable manifold > harmonic map

geometry > differential geometry > differentiable manifold > harmonic map

topology > differential topology > differentiable manifold > harmonic map

Preferred term

harmonic map

Definition(s)

In the mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy a certain nonlinear partial differential equation. This partial differential equation for a mapping also arises as the Euler-Lagrange equation of a functional called the Dirichlet energy. As such, the theory of harmonic maps contains both the theory of unit-speed geodesics in Riemannian geometry and the theory of harmonic functions.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Harmonic_map)

Broader concept(s)

differentiable manifold

Related concept(s)

Riemannian manifold

In other languages

application harmonique

French

URI

http://data.loterre.fr/ark:/67375/PSR-BJT46KVS-9

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