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Minimal surfaces in tori by Weyl groups


Authors: T. Nagano and B. Smyth
Journal: Proc. Amer. Math. Soc. 61 (1976), 102-104
MSC: Primary 53C40
DOI: https://doi.org/10.1090/S0002-9939-1976-0431047-3
MathSciNet review: 0431047
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Abstract: We report a method of constructing compact minimal surfaces immersed in flat Riemannian tori of arbitrary dimension $ n \geqslant 3$ by the use of the Weyl groups of compact simple Lie groups, inspired by H. A. Schwarz [5].


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  • [1] N. Bourbaki, Eléments de mathématique, Fasc. 34, Groupes et algèbres de Lie, Chaps. 4, 5, 6, Actualités Sci. Indust., no. 1337, Hermann, Paris, 1968. MR 39 #1590. MR 0240238 (39:1590)
  • [2] B. Lawson, Lectures on minimal submanifolds, Inst. Mat. Pura Appl., Rio de Janeiro, 1973.
  • [3] T. Nagano and B. Smyth, Minimal submanifolds in flat tori, Comment. Math. Helv. 50 (1975), 249-265. MR 0390974 (52:11797)
  • [4] Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold, New York, 1969. MR 41 #934. MR 0256278 (41:934)
  • [5] H. A. Schwarz, Gesammelte mathematische Abhandlungen, Vol. I, Springer-Verlag, Berlin, 1890; English transl., Chelsea, New York.
  • [6] B. Stessmann, Periodische Minimalflächen, Math. Z. 38 (1934), 417-442. MR 1545457

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0431047-3
Keywords: Minimal surface, Weyl group, torus
Article copyright: © Copyright 1976 American Mathematical Society

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