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On an explicit characterization of spherical curves


Author: Yung Chow Wong
Journal: Proc. Amer. Math. Soc. 34 (1972), 239-242
MSC: Primary 53A05
DOI: https://doi.org/10.1090/S0002-9939-1972-0295224-3
Erratum: Proc. Amer. Math. Soc. 38 (1973), 668.
MathSciNet review: 0295224
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Abstract: It will be proved that the ``explicit characterization'' of spherical curves recently obtained by S. Breuer and D. Gottlieb (Proc. Amer. Math. Soc. 27 (1971), pp. 126-127) is, without any precondition on the curvature and torsion, a necessary and sufficient condition for a curve to be a spherical curve. The proof is based on an earlier result of the present author on spherical curves (Monatsh. Math. 67 (1963), pp. 363-365).


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

  • [1] S. Breuer and D. Gottlieb, Explicit characterization of spherical curves, Proc. Amer. Math. Soc. 27 (1971), 126-127. MR 41 #5165. MR 0270275 (42:5165)
  • [2] D. J. Struik, Lectures on classical differential geometry, Addison-Wesley, Reading, Mass., 1950. MR 12, 127. MR 0036551 (12:127f)
  • [3] C. E. Weatherburn, Differential geometry of three dimensions. Vol. 1, Cambridge Univ. Press, London, 1931.
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  • [5] Y. C. Wong and H. F. Lai, A critical examination of the theory of curves in three dimensional differential geometry, Tôhoku Math. J. (2) 19 (1967), 1-31. MR 35 #4825. MR 0213973 (35:4825)

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DOI: https://doi.org/10.1090/S0002-9939-1972-0295224-3
Keywords: Spherical curve, curvature, torsion, nowhere zero
Article copyright: © Copyright 1972 American Mathematical Society

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