# The rectifying developable and the spherical Darboux image of a space curve

Shyuichi Izumiya; Haruyo Katsumi; Takako Yamasaki

Banach Center Publications (1999)

- Volume: 50, Issue: 1, page 137-149
- ISSN: 0137-6934

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topIzumiya, Shyuichi, Katsumi, Haruyo, and Yamasaki, Takako. "The rectifying developable and the spherical Darboux image of a space curve." Banach Center Publications 50.1 (1999): 137-149. <http://eudml.org/doc/209002>.

@article{Izumiya1999,

abstract = {In this paper we study singularities of certain surfaces and curves associated with the family of rectifying planes along space curves. We establish the relationships between singularities of these subjects and geometric invariants of curves which are deeply related to the order of contact with helices.},

author = {Izumiya, Shyuichi, Katsumi, Haruyo, Yamasaki, Takako},

journal = {Banach Center Publications},

keywords = {regular space curves; non-degeneracy},

language = {eng},

number = {1},

pages = {137-149},

title = {The rectifying developable and the spherical Darboux image of a space curve},

url = {http://eudml.org/doc/209002},

volume = {50},

year = {1999},

}

TY - JOUR

AU - Izumiya, Shyuichi

AU - Katsumi, Haruyo

AU - Yamasaki, Takako

TI - The rectifying developable and the spherical Darboux image of a space curve

JO - Banach Center Publications

PY - 1999

VL - 50

IS - 1

SP - 137

EP - 149

AB - In this paper we study singularities of certain surfaces and curves associated with the family of rectifying planes along space curves. We establish the relationships between singularities of these subjects and geometric invariants of curves which are deeply related to the order of contact with helices.

LA - eng

KW - regular space curves; non-degeneracy

UR - http://eudml.org/doc/209002

ER -

## References

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- [6] G. Ishikawa, Topological classification of the tangent developable of space curves, Hokkaido Univ. Preprint Series 341 (1996).
- [7] J. Koenderink, Solid Shape, MIT Press, Cambridge, MA, 1990.
- [8] D. Mond, On the tangent developable of a space curve, Math. Proc. Cambridge Philos. Soc. 91 (1982), 351-355. Zbl0495.58005
- [9] D. Mond, Singularities of the tangent developable surface of a space curve, Quart. J. Math. Oxford Ser. (2) 40 (1989), 79-91. Zbl0706.58006
- [10] I. R. Porteous, The normal singularities of submanifold, J. Differential Geom. 5 (1971), 543-564. Zbl0226.53010
- [11] I. R. Porteous, Geometric Differentiation for the Intelligence of Curves and Surfaces, Cambridge Univ. Press, Cambridge, 1994. Zbl0806.53001
- [12] O. P. Shcherbak, Projectively dual space curves and Legendre singularities (in Russian), Trudy Tbiliss. Univ. 232-233 (1982), 280-336; English translation: Selecta Math. Soviet. 5 (1986), 391-421.

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