Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606752 | Differential Geometry and its Applications | 2007 | 7 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Qilin Yang,