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A closed surface of genus one in $ E\sp 3$ cannot contain seven circles through each point


Author: Nobuko Takeuchi
Journal: Proc. Amer. Math. Soc. 100 (1987), 145-147
MSC: Primary 53A05; Secondary 53C45
DOI: https://doi.org/10.1090/S0002-9939-1987-0883418-6
MathSciNet review: 883418
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Abstract | References | Similar Articles | Additional Information

Abstract: There exists a closed surface of genus one in $ {E^3}$ which contains six cirlces through each point, but any closed surface of genus one in $ {E^3}$ cannot contain seven circles through each point.


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

  • [1] R. Blum, Circles on surfaces in the Euclidean $ 3$-space, Lecture Notes in Math., vol. 792, Springer, 1980, pp. 213-221. MR 585871 (83c:53004)
  • [2] K. Ogiue and R. Takagi, A submanifold which contains many extrinsic circles, Tsukuba J. Math. 8 (1984), 171-182. MR 747454 (85i:53023)
  • [3] N. Takeuchi, A sphere as a surface which contains many circles, J. Geom. 24 (1985), 123-130. MR 793276 (86k:53007)
  • [4] D. Rolfsen, Knots and links, Math. Lecture Series No. 7, Publish or Perish, Berkeley, Calif, 1976. MR 0515288 (58:24236)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0883418-6
Keywords: A closed surface of genus one, circles
Article copyright: © Copyright 1987 American Mathematical Society

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