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A sharp Eells-Sampson type theorem under positive sectional curvature upper bounds
Published 27 Mar 2024 in math.DG | (2403.18596v2)
Abstract: We prove an extension of Eells and Sampson's rigidity theorem for harmonic maps from a closed manifold of non-negative Ricci curvature to a manifold of non-positive sectional curvature. We give an application of our result in the setting of harmonic-Einstein (or Ricci-harmonic) metrics and as a consequence we recover a classical rigidity result of Hamilton for the problem of prescribed positive definite Ricci curvature.
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