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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[C1]Calabi, E.: Isometric imbeddings of complex manifolds. Ann. Math.58, 1–23 (1953).
[C2]Calabi, E.: Quelques applications l'analyse complexe aux surfaces d'aire minima (together with Topics Complex Manifolds byH. Rossi). Les Presses de l'Université de Montreal, 1968.
[H-O]Hoffmann, D., Osserman, R.: The Geometry of the Generalized Gauss Map. Memoirs of the A. M. S., No. 236, 1980.
[L]Lawson, H. B. Jr.: Lectures on Minimal Submanifolds, Vol. I. Berkeley, CA: Publish or Perish, Inc.
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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