Pseudo-harmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds with nonpositive sectional curvature |
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Authors: | Email author" target="_blank">Yibin?RenEmail author Guilin?Yang |
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Institution: | 1.College of Mathematics, Physics and Information Engineering,Zhejiang Normal University,Jinhua,People’s Republic of China;2.Dipartimento di Matematica, Informatica ed Economia,Università degli Studi della Basilicata,Potenza,Italy |
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Abstract: | In this paper, we use heat flow method to prove the existence of pseudo-harmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds with nonpositive sectional curvature, which is a generalization of Eells–Sampson’s existence theorem. Furthermore, when the target manifold has negative sectional curvature, we analyze horizontal energy of geometric homotopy of two pseudo-harmonic maps and obtain that if the image of a pseudo-harmonic map is neither a point nor a closed geodesic, then it is the unique pseudo-harmonic map in the given homotopic class. This is a generalization of Hartman’s theorem. |
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