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.
Taiwanese J. Math.
20(5):
1053-1064
(2016).
DOI: 10.11650/tjm.20.2016.7247