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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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On the differential geometry of closed space curves
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by Werner Fenchel PDF
Bull. Amer. Math. Soc. 57 (1951), 44-54
References
  • Wilhelm Blaschke, Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Band I. Elementare Differentialgeometrie, Dover Publications, New York, N.Y., 1945 (German). 3d ed. MR 0015247
    • 2. W. Blaschke, Vorlesungen über Integralgeometrie II, Leipzig and Berlin, 1937; New York, 1950.
  • Karol Borsuk, Sur la courbure totale des courbes fermées, Ann. Soc. Polon. Math. 20 (1947), 251–265 (1948) (French). MR 0025757
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  • Werner Fenchel, Über Krümmung und Windung geschlossener Raumkurven, Math. Ann. 101 (1929), no. 1, 238–252 (German). MR 1512528, DOI 10.1007/BF01454836
    • 6. W. Fenchel, Geschlossene Raumkurven mit vorgeschriebenem Tangentenbild, Jber. Deutschen Math. Verein. vol. 39 (1930) pp. 183-185. 7. W. Fenchel, Über einen Jacobischen Satz der Kurventheorie, Tôhoku Math. J. vol. 39 (1934) pp. 95-97. 8. C. G. J. Jacobi, Über einige merkwürdige Curventheoreme, Astronomische Nachrichten vol. 20 (1842) pp. 115-120; Gesammelte Werke, vol. 7, pp. 34-39.
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    • 10. T. Levi-Civita, Curve chiuse a parallelismo monodromo sopra la sfera, Pontificia Academia Scientiarum Acta vol. 87 (1934) 10 pp. 11. H. Liebmann, Elementarer Beweis des Fenchelschen Satzes über die Krümmung geschlossener Raumkurven, Preuss. Akad. Wiss. Sitzungsber. (1929) pp. 292-293.
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    • 13. G. Scheffers, Anwendung der Differential- und Integralrechnung auf Geometrie, vol. 1, Einführung in die Theorie der Curven in der Ebene und im Raume, Leipzig, 1901, pp. 240-251.
  • W. Scherrer, Über das Hauptnormalenbild einer Raumkurve, Comment. Math. Helv. 19 (1946), 115–133 (German). MR 18000, DOI 10.1007/BF02565952
    • 15. B. Segre, Sui circoli geodetici di una superficie a curvatura totale costante, che contengono nell’interno una linea assegnata, Bollettino della Unione Matematica Italiana vol. 13 (1934) pp. 279-283.
  • B. Segre, Sulla torsione integrale delle curve chiuse sghembe, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 3 (1947), 422–426 (Italian). MR 26832
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Additional Information
  • Journal: Bull. Amer. Math. Soc. 57 (1951), 44-54
  • DOI: https://doi.org/10.1090/S0002-9904-1951-09440-9
  • MathSciNet review: 0040040