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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal surfaces in tori by Weyl groups
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by T. Nagano and B. Smyth PDF
Proc. Amer. Math. Soc. 61 (1976), 102-104 Request permission

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
  • 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 [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
  • B. Lawson, Lectures on minimal submanifolds, Inst. Mat. Pura Appl., Rio de Janeiro, 1973.
  • Tadashi Nagano and Brian Smyth, Minimal varieties and harmonic maps in tori, Comment. Math. Helv. 50 (1975), 249–265. MR 390974, DOI 10.1007/BF02565749
  • Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. MR 0256278
  • H. A. Schwarz, Gesammelte mathematische Abhandlungen, Vol. I, Springer-Verlag, Berlin, 1890; English transl., Chelsea, New York.
  • Berthold Steßmann, Periodische Minimalflächen, Math. Z. 38 (1934), no. 1, 417–442 (German). MR 1545457, DOI 10.1007/BF01170644
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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