Harmonic maps from closed Riemannian manifolds with positive scalar curvature |
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Authors: | Qilin Yang |
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Affiliation: | Mathematical Department, Tsinghua University, 100084, Beijing, PR China |
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Abstract: | It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorem cannot hold in general. This raises the question: “What information can we obtain from the existence of non-constant harmonic map?” This paper gives answer to this problem; the results obtained are optimal. |
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Keywords: | 53C43 58E20 |
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