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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 883418
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0883418-6
PII: S 0002-9939(1987)0883418-6
Keywords: A closed surface of genus one, circles
Article copyright: © Copyright 1987 American Mathematical Society