A sharp Eells-Sampson type theorem under positive sectional curvature upper bounds

Giulio Colombo; Marco Mariani; Marco Rigoli

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arXiv · 2403.18596

A sharp Eells-Sampson type theorem under positive sectional curvature upper bounds

Giulio Colombo·Marco Mariani·Marco Rigoli

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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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Giulio Colombo, Marco Mariani, Marco Rigoli. 2024-03-27. A sharp Eells-Sampson type theorem under positive sectional curvature upper bounds. https://arxiv.org/abs/2403.18596

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