New Characterizations of the Clifford Torus and the Great Sphere

Symmetry

SunMi Jung¹  YoungHo Kim¹  Jinhua Qian² 

[1] Department of Mathematics, Kyungpook National University, Daegu 41566, Korea;Department of Mathematics, Northeastern University, Shenyang 110004, China;

关键词: Clifford torus;    spherical Gauss map;    finite-type;    pointwise 1-type spherical Gauss map;   

DOI  :  10.3390/sym11091076

来源: DOAJ

【 摘 要 】

In studying spherical submanifolds as submanifolds of a round sphere, it is more relevant to consider the spherical Gauss map rather than the Gauss map of those defined by the oriented Grassmannian manifold induced from their ambient Euclidean space. In that sense, we study ruled surfaces in a three-dimensional sphere with finite-type and pointwise 1-type spherical Gauss map. Concerning integrability and geometry, we set up new characterizations of the Clifford torus and the great sphere of 3-sphere and construct new examples of spherical ruled surfaces in a three-dimensional sphere.

【 授权许可】

Unknown