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A remark concerning a mechanical characterization of the sphere

Author: Paris Pamfilos
Journal: Proc. Amer. Math. Soc. 96 (1986), 648-650
MSC: Primary 53A17; Secondary 53A05
MathSciNet review: 826496
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Abstract: It is shown that if a (sufficiently) small ball rolls freely without sliding on a compact surface in such a way that its center moves with constant in magnitude velocity for every initial condition, then the surface must be a sphere.

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

  • [1] F. Noether, Ueber die rollende Bewegung einer Kugel auf Rotationsflächen, Dissertation, München, 1909.
  • [2] J. I. Neimark and N. A. Fufaev, Dynamics of nonholonomic systems, Transl. Math. Monos., vol. 33, Amer. Math. Soc., Providence, R.I., 1972.
  • [3] Barrett O’Neill, Elementary differential geometry, Academic Press, New York-London, 1966. MR 0203595

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Article copyright: © Copyright 1986 American Mathematical Society

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