Displaying similar documents to “Minimizing Harmonic Mappings form a surface perfored with small holes into a riemannian manifold.”

A curvature identity on a 6-dimensional Riemannian manifold and its applications

Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa (2017)

Czechoslovak Mathematical Journal

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We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional...

Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

Annales de l'institut Fourier

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A harmonic morphism f : M → N between Riemannian manifolds M and N is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim M ≥ dim N , since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where d f vanishes. Every non-constant harmonic morphism is shown to be...