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• W2269023558 abstract "Fifty years ago, Eells and Sampson have proved a famous theorem which they argued that any harmonic mapping $f:(M,g) rightarrow (bar{M},bar{g})$ is totally geodesic if $(M, g)$ is a compact manifold with the nonnegative Ricci tensor and the section curvature of $(bar{M},bar{g})$ is nonpositive. Moreover, other main results of the theory of harmonic mappings in the large are the results on harmonic maps into nonpositively curved Riemannian manifolds. In our paper we develop a theory of harmonic mappings into Riemannian manifolds with nonnegative sectional curvature. In particular, we will prove that any harmonic map between Riemannian manifolds $f:(M,g) rightarrow (bar{M},bar{g})$ is totally geodesic if the section curvature of $(bar{M},bar{g})$ is nonnegative and $(M, g)$ is a compact manifold with the Ricci tensor $Ric geq f^{*}bar{Ric}$ for the pullback $f^{*}bar{Ric}$ of the Ricci tensor $bar{Ric}$ by $f$. The above scheme will be extended to a harmonic mapping of a complete manifold to a manifold with the nonnegative sectional curvature. Moreover, we will obtain interesting corollaries from our results." @default.
• W2269023558 created "2016-06-24" @default.
• W2269023558 creator A5080712497 @default.
• W2269023558 creator A5081384789 @default.
• W2269023558 date "2015-08-26" @default.
• W2269023558 modified "2023-09-27" @default.
• W2269023558 title "Harmonic Mappings into non-negatively curved Riemannian manifolds" @default.
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