Normal developable surfaces of a surface along a direction curve. (English) Zbl 1455.53028
Summary: We construct a developable surface normal to a surface along a curve on the surface. We choose the curve as the normal direction curve on which the new surface is formed in Euclidean space. We obtain some results about the uniqueness and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize singularities.
MSC:
| 53A05 | Surfaces in Euclidean and related spaces |
| 53A04 | Curves in Euclidean and related spaces |
| 57R45 | Singularities of differentiable mappings in differential topology |
Keywords:
normal developable surfaces; curves on surfaces; ruled surfaces; direction curve; singularitiesSoftware:
CandSReferences:
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