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1999 | 50 | 1 | 137-149
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
50
Numer
1
Strony
137-149
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
  • Department of Mathematics, Ochanomizu University, Bunkyou-ku Otsuka Tokyo 112-8610, Japan
  • Department of Mathematics, Ochanomizu University, Bunkyou-ku Otsuka Tokyo 112-8610, Japan
Bibliografia
  • [1] J. W. Bruce, P. J. Giblin, Curves and Singularities, 2nd ed., Cambridge Univ. Press, Cambridge, 1992.
  • [2] M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, 1976.
  • [3] J. P. Cleave, The form of the tangent developable at points of zero torsion on space curves, Math. Proc. Cambridge Philos. Soc. 88 (1980), 403-407.
  • [4] G. Ishikawa, Determinacy of envelope of the osculating hyperplanes to a curve, Bull. London Math. Soc. 25 (1993), 603-610.
  • [5] G. Ishikawa, Developable of a curve and its determinacy relative to the osculation-type, Quart. J. Math. Oxford Ser. (2) 46 (1995), 437-451.
  • [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.
  • [9] D. Mond, Singularities of the tangent developable surface of a space curve, Quart. J. Math. Oxford Ser. (2) 40 (1989), 79-91.
  • [10] I. R. Porteous, The normal singularities of submanifold, J. Differential Geom. 5 (1971), 543-564.
  • [11] I. R. Porteous, Geometric Differentiation for the Intelligence of Curves and Surfaces, Cambridge Univ. Press, Cambridge, 1994.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv50z1p137bwm
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