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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A new foundation of the projective differential theory of curves in five-dimensional space


Author: Su-Cheng Chang
Journal: Trans. Amer. Math. Soc. 59 (1946), 132-165
MSC: Primary 53.0X
MathSciNet review: 0015262
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  • [1] Bompiani, Per lo studio proiettivo-differenziale della singolarità, Boll. dell'Unione Mat. Italiana vol. 5 (1926) pp. 118-120.
  • [2] Chang, A generalization of sextactic points of a plane curve, not yet published.
  • [3] Su-Cheng Chang, The point of inflexion of a plane curve, Duke Math. J. 9 (1942), 823–832. MR 0007607 (4,167a)
  • [4] -, On the point of inflexion of a space curve, To be published in Revista de Tucumàn, Argentina.
  • [5] -, On the singularity $ S_1^4$ of a plane curve, not yet published.
  • [6] Su-Cheng Chang, The singularity 𝑆₁^{𝑚} of a plane curve, Duke Math. J. 9 (1942), 833–845. MR 0007608 (4,167b)
  • [7] -, Researches on the projective differential theory of singular points, I, II, to be published in Amer. J. Math.
  • [8] Ernest P. Lane, The neighborhood of a sextactic point on a plane curve, Duke Math. J. 1 (1935), no. 3, 287–292. MR 1545877, http://dx.doi.org/10.1215/S0012-7094-35-00119-3
  • [9] T. Levi-Civita and G. Fubini, Sulle curve analoghe al circolo osculatore quando si passa da tre a quattro punti infinitamente vicini, Ann. Mat. Pura Appl. 7 (1929), no. 1, 193–211 (Italian). MR 1553142, http://dx.doi.org/10.1007/BF02409974
  • [10] Sannia, Nuova trattazione della geometria proiettiva differenziale delle curve sghembe, Memoir I, Annali di Matematica (4) vol. 1 (1924) pp. 1-18; Memoir II, ibid, vol.3 (1926) pp. 1-25.
  • [11] Su, Contributions to the projective theory of curves in space of five dimensions, to be published in Duke Math. J.; an abstract of this paper will appear in Science Record, Academia Sinica.
  • [12] -, Note on the projective differential geometry of space curves, Journal of the Chinese Mathematical Society vol. 1 (1937) pp. 98-137.
  • [13] Vychyclo, Interpretazione geometrica della curvatura proiettiva della curve plane, Bollettino dell'Unione Matematica Italiana vol. 17 (1938) pp. 74-77.
  • [14] F. Vycichlo, Sur une interprétation géométrique de la courbure projective des courbes planes, Bull. Soc. Math. France 64 (1936), 87–98 (French). MR 1505050
  • [15] Wilczynski, Projective differential geometry of curves and ruled surfaces, Teubner, 1906.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1946-0015262-4
PII: S 0002-9947(1946)0015262-4
Article copyright: © Copyright 1946 American Mathematical Society