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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- [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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