A generalization of the isoperimetric inequality on $S^ 2$ and flat tori in $S^ 3$
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- by Kazuyuki Enomoto
- Proc. Amer. Math. Soc. 120 (1994), 553-558
- DOI: https://doi.org/10.1090/S0002-9939-1994-1163333-7
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Abstract:
A geometric inequality is proved for closed curves on ${S^2}$ which are regularly homotopic to simple closed curves. This generalizes the classical isoperimetric inequality for simple closed curves on ${S^2}$. The proof is based on the study of flat tori in ${S^3}$ and their images under the Gauss map.References
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- Kazuyuki Enomoto, Global properties of the Gauss image of flat surfaces in $\textbf {R}^4$, Kodai Math. J. 10 (1987), no. 3, 272–284. MR 929986, DOI 10.2996/kmj/1138037457
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- Joel L. Weiner, Flat tori in $S^3$ and their Gauss maps, Proc. London Math. Soc. (3) 62 (1991), no. 1, 54–76. MR 1078213, DOI 10.1112/plms/s3-62.1.54
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 553-558
- MSC: Primary 53A04; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1994-1163333-7
- MathSciNet review: 1163333