On an explicit characterization of spherical curves
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- by Yung Chow Wong PDF
- Proc. Amer. Math. Soc. 34 (1972), 239-242 Request permission
Erratum: Proc. Amer. Math. Soc. 38 (1973), 668.
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
- Shlomo Breuer and David Gottlieb, Explicit characterization of spherical curves, Proc. Amer. Math. Soc. 27 (1971), 126–127. MR 270275, DOI 10.1090/S0002-9939-1971-0270275-2
- Dirk J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Press, Inc., Cambridge, Mass., 1950. MR 0036551 C. E. Weatherburn, Differential geometry of three dimensions. Vol. 1, Cambridge Univ. Press, London, 1931.
- Yung-chow Wong, A global formulation of the condition for a curve to lie in a sphere, Monatsh. Math. 67 (1963), 363–365. MR 155237, DOI 10.1007/BF01299587
- Yung-chow Wong and Hon-fei Lai, A critical examination of the theory of curves in three dimensional differential geometry, Tohoku Math. J. (2) 19 (1967), 1–31. MR 213973, DOI 10.2748/tmj/1178243344
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 239-242
- MSC: Primary 53A05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0295224-3
- MathSciNet review: 0295224