A closed surface of genus one in $E^ 3$ cannot contain seven circles through each point
HTML articles powered by AMS MathViewer
- by Nobuko Takeuchi PDF
- Proc. Amer. Math. Soc. 100 (1987), 145-147 Request permission
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
- Richard Blum, Circles on surfaces in the Euclidean $3$-space, Geometry and differential geometry (Proc. Conf., Univ. Haifa, Haifa, 1979), Lecture Notes in Math., vol. 792, Springer, Berlin-New York, 1980, pp. 213–221. MR 585871
- Koichi Ogiue and Ryoichi Takagi, A submanifold which contains many extrinsic circles, Tsukuba J. Math. 8 (1984), no. 1, 171–182. MR 747454, DOI 10.21099/tkbjm/1496159953
- Nobuko Takeuchi, A sphere as a surface which contains many circles, J. Geom. 24 (1985), no. 2, 123–130. MR 793276, DOI 10.1007/BF01220483
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
Additional Information
- © Copyright 1987 American Mathematical Society
- 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