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Harmonic morphisms as unit normal bundles¶of minimal surfaces

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Abstract:

Let be an isometric immersion between Riemannian manifolds and be the unit normal bundle of f. We discuss two natural Riemannian metrics on the total space and necessary and sufficient conditions on f for the projection map to be a harmonic morphism. We show that the projection map of the unit normal bundle of a minimal surface in a Riemannian manifold is a harmonic morphism with totally geodesic fibres.

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Authors and Affiliations

  1. Centre for Mathematical Sciences, University of Lund, Box 118,¶S-221 00 Lund, Sweden. e-mail: Sigmundur.Gudmundsson@math.lu.se, , , , , , SE

    Sigmundur Gudmundsson

  2. School of Mathematical Sciences, Peking University, Beijing 100871, Peoples Republic of China. e-mail: moxh@pku.edu.cn, , , , , , CN

    Xiaohuan Mo

Authors
  1. Sigmundur Gudmundsson
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  2. Xiaohuan Mo
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Received: 6 February 1999

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Gudmundsson, S., Mo, X. Harmonic morphisms as unit normal bundles¶of minimal surfaces. manuscripta math. 100, 323–333 (1999). https://doi.org/10.1007/s002290050204

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  • DOI: https://doi.org/10.1007/s002290050204

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