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Harmonic maps from a Riemannian manifold with a pole into an Hadamard manifold with negative sectional curvatures

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Abstract

In this paper we show a nonexistence result for harmonic maps with a rotational nondegeneracy condition from a Riemannian manifoldM with polep 0 to a negatively curved Hadamard manifold under the condition that the metric tensor ofM is bounded and that the sectional curvature ofM at a pointp is bounded from below by −c dist(p 0,p)−2 (c: a positive constant) as dist(p 0,p)→∞.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Liberal Arts, Shizuoka University, 422, Ohya, Shizuoka, Japan

    Atsushi Tachikawa

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  1. Atsushi Tachikawa
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Partly supported by Grants-in-Aid for Scientific Research, The Ministry of Education, Science and Culture, Japan

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Tachikawa, A. Harmonic maps from a Riemannian manifold with a pole into an Hadamard manifold with negative sectional curvatures. Manuscripta Math 74, 69–81 (1992). https://doi.org/10.1007/BF02567658

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  • DOI: https://doi.org/10.1007/BF02567658

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