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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Contributions to the theory of surfaces in a 4-space of constant curvature
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Trans. Amer. Math. Soc. 59 (1946), 467-507 Request permission

Erratum: Trans. Amer. Math. Soc. 60 (1946), 550.
References
    M. Bôcher, Introduction to higher algebra, New York, 1908. O. Borůvka, Sur une classe de surfaces minima plongées dans un espace à quatre dimensions à courboure constante, Bulletin international Česká akademie véd a umĕní v Praze vol. 29 (1928) pp. 256-277. R. Calapso, Sulle reti di Voss di uno spazio lineare quadri dimensionale, Rendiconti Seminario matematico Roma (4) vol. 2 (1938) pp. 276-311. —, Sulle deformazione delle reti di Voss di un ${S_4}$ euclideo, Atti Accademia nazionale dei Lincei (4) vol. 28 (1939) pp. 231-236.
  • Nathaniel Coburn, Surfaces in four-space of constant curvature, Duke Math. J. 5 (1939), no. 1, 30–38. MR 1546103, DOI 10.1215/S0012-7094-39-00504-1
  • Luther Pfahler Eisenhart, Minimal Surfaces in Euclidean Four-Space, Amer. J. Math. 34 (1912), no. 3, 215–236. MR 1506152, DOI 10.2307/2370220
  • —, Differential geometry, New York, 1909. —, Riemannian geometry, Princeton, 1926.
  • W. C. Graustein, Invariant methods in classical differential geometry, Bull. Amer. Math. Soc. 36 (1930), no. 8, 489–521. MR 1561985, DOI 10.1090/S0002-9904-1930-04979-4
  • J. Knoblauch, Grundlagen der Differentialgeometrie, Leipzig, 1913.
  • Karl Kommerell, Riemannsche Flächen im ebenen Raum von vier Dimensionen, Math. Ann. 60 (1905), no. 4, 548–596 (German). MR 1511325, DOI 10.1007/BF01561096
  • S. Kwietniewski, Über Flächen des vierdimensionalen Raumes, deren sämtliche Tangentialebenen untereinander gleichwinklig sind, und ihre Beziehung zu den ebenen Kurven, Dissertation, Zürich. C. L. E. Moore, and E. B. Wilson, Differential geometry of two-dimensional surfaces in hyperspace, Proceedings of the American Academy of Arts and Sciences vol. 52 (1916) pp. 267-368. G. Ricci, Lezioni sulla teoria della superficie, Verona and Padova, Druker, 1898. J. A. Schouten, and D. J. Struik, Einführung in die neueren Methoden der Differential-geometrie II, Batavia, 1938.
  • C. Tompkins, Isometric embedding of flat manifolds in Euclidean space, Duke Math. J. 5 (1939), no. 1, 58–61. MR 1546106, DOI 10.1215/S0012-7094-39-00507-7
  • C. Zitto, Reti di Voss a curvatura nulla di un ${S_4}$ euclideo, Atti Acad. Pelororitana vol. 41 (1939) pp. 44-47.
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Additional Information
  • © Copyright 1946 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 59 (1946), 467-507
  • MSC: Primary 53.0X
  • DOI: https://doi.org/10.1090/S0002-9947-1946-0016231-0
  • MathSciNet review: 0016231