Taiwanese Journal of Mathematics

Characterizations of Tori in $3$-spheres

Dong-Soo Kim, Young Ho Kim, and Dae Won Yoon

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Using the $II$-metric and the $II$-Gauss map on a surface derived from the non-degenerate second fundamental form of a surface in the sphere, we establish some characterizations of compact surfaces including the spheres and the tori in the $3$-dimensional unit sphere.

Article information

Taiwanese J. Math., Volume 20, Number 5 (2016), 1053-1064.

First available in Project Euclid: 1 July 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53B25: Local submanifolds [See also 53C40] 53C40: Global submanifolds [See also 53B25]

torus principal curvatures $II$-metric finite type immersion $II$-Gauss map


Kim, Dong-Soo; Kim, Young Ho; Yoon, Dae Won. Characterizations of Tori in $3$-spheres. Taiwanese J. Math. 20 (2016), no. 5, 1053--1064. doi:10.11650/tjm.20.2016.7247. https://projecteuclid.org/euclid.twjm/1498874516

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