Generalized osculating-type ruled surfaces of singular curves. (English) Zbl 1529.58015
Summary: In this study, we introduce generalized osculating-type ruled surfaces of special singular curves. We give some theories and results about the geometric structure of the surface. In addition, the singular point classes of the surface are examined, and the conditions for being a cross-cap surface are expressed. Generalized osculating-type ruled surface is considered as a framed surface and its basic invariants are found and some results are given. Finally, we give some examples and figures to support the theories.
{© 2023 John Wiley & Sons, Ltd.}
{© 2023 John Wiley & Sons, Ltd.}
MSC:
| 58K05 | Critical points of functions and mappings on manifolds |
| 53A05 | Surfaces in Euclidean and related spaces |
| 57R45 | Singularities of differentiable mappings in differential topology |
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