Extrinsic flat surfaces along a curve on a surface in the unit three-sphere. (English) Zbl 1453.53008
Authors’ abstract: In this paper, we consider the curves on the surface in the unit 3-sphere. For a regular curve on a surface in the unit 3-sphere, we have a moving frame along the curve which is called a spherical Darboux frame. We induce two special vector fields along the curve with respect to the spherical Darboux frame and investigate the singularities of extrinsic flat great circular surfaces associated with these vector fields.
Reviewer: Ergin Bayram (Samsun)
MSC:
| 53A04 | Curves in Euclidean and related spaces |
| 53A07 | Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces |
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