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Pseudo-harmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds with nonpositive sectional curvature

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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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Acknowledgements

The authors would like to express their thanks to Professor Yuxin Dong for constant encouragements and valuable discussions.

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Authors and Affiliations

  1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Yibin Ren

  2. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, 85100, Potenza, Italy

    Guilin Yang

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  1. Yibin Ren
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  2. Guilin Yang
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Correspondence to Yibin Ren.

Additional information

Communicated by A. Chang.

Supported by NSFC Tianyuan fund for Mathematics Grant No. 11626217.

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Ren, Y., Yang, G. Pseudo-harmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds with nonpositive sectional curvature. Calc. Var. 57, 128 (2018). https://doi.org/10.1007/s00526-018-1411-1

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  • DOI: https://doi.org/10.1007/s00526-018-1411-1

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