Stable complete minimal surfaces in hyperkähler manifolds |
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Authors: | Claudio Arezzo |
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Institution: | (1) University of Warwick, United Kingdom;(2) Italy |
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Abstract: | In this paper we prove that an isometric stable minimal immersion of a complete oriented surface into a hyperkähler 4-manifold is holomorphic with respect to an orthogonal complex structure, if it satisfies a Bernstein-type assumption on the Gauss-lift. This result generalizes a theorem of Micallef for minimal surfaces in the euclidean 4-space. An example found by Atiyah and Hitchin shows that the assumption on the Gauss-lift is necessary. |
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Keywords: | minimal surfaces kä hler angle hyperkä hler manifolds |
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