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Harmonie reflections

Lieven Vanhecke;  Maria-Elena Vazquez-Abal — 1988

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study local reflections ϕ σ with respect to a curve σ in a Riemannian manifold and prove that σ is a geodesic if ϕ σ is a harmonic map. Moreover, we prove that the Riemannian manifold has constant curvature if and only if ϕ σ is harmonic for all geodesies σ .

Harmonie reflections

Lieven Vanhecke;  Maria-Elena Vazquez-Abal — 1988

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

We study local reflections ϕ σ with respect to a curve σ in a Riemannian manifold and prove that σ is a geodesic if ϕ σ is a harmonic map. Moreover, we prove that the Riemannian manifold has constant curvature if and only if ϕ σ is harmonic for all geodesies σ .

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