Great circular surfaces in the three-sphere. (English) Zbl 1218.53054
Summary: We consider a special class of the surfaces in the 3-sphere defined by one-parameter families of great circles. We give a generic classification of singularities of such surfaces and investigate the geometric meanings from the view point of spherical geometry.
MSC:
| 53C40 | Global submanifolds |
| 57R45 | Singularities of differentiable mappings in differential topology |
| 58K40 | Classification; finite determinacy of map germs |
Keywords:
3-sphere; spherical geometry; great circle; great circular surface; extrinsic flat surface; singularitiesReferences:
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