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Complex analytic curves and maximal surfaces

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Abstract

Maximal immersions of a surfaceM 2 inton-dimensional Lorentz space which are isometric to a fixed holomorphic mapping ofM 2 into complex Lorentz space are determined. The main tool is an adaption of Calabi's Rigidity Theorem. Such an adaption is necessary because of the existence of degenerate hyperplanes in complex Lorentz space.

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References

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  • [L]Lawson, H. B. Jr.: Lectures on Minimal Submanifolds, Vol. I. Berkeley, CA: Publish or Perish, Inc.

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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, 06268, Storrs, CT, USA

    K. Abe

  2. Department of Mathematics, Wellesley College, 02181, Wellesley, MA, USA

    M. A. Magid

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  1. K. Abe
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  2. M. A. Magid
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Partially supported by a grant from Wellesley College.

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Abe, K., Magid, M.A. Complex analytic curves and maximal surfaces. Monatshefte für Mathematik 108, 255–276 (1989). https://doi.org/10.1007/BF01501129

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  • DOI: https://doi.org/10.1007/BF01501129

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