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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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].


References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968 (French). MR 0240238
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  • [5] H. A. Schwarz, Gesammelte mathematische Abhandlungen, Vol. I, Springer-Verlag, Berlin, 1890; English transl., Chelsea, New York.
  • [6] Berthold Steßmann, Periodische Minimalflächen, Math. Z. 38 (1934), no. 1, 417–442 (German). MR 1545457, https://doi.org/10.1007/BF01170644

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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