PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 50 | 1 | 277-285
Tytuł artykułu

Curvatures of conflict surfaces in Euclidean 3-space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane, established by Siersma [3]. In the present case a conflict surface arises, equidistant from the given convex sets. The Gaussian, mean curvatures and the location of umbilic points on the conflict surface are determined here. Initial results on the Darbouxian type of umbilic points on conflict surfaces are also established. The results are expressed in terms of the principal directions and on the curvatures of the borders of the given convex sets.
Słowa kluczowe
Rocznik
Tom
50
Numer
1
Strony
277-285
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Instituto de Matemática e Estatí stica, Universidade de São Paulo, Caixa Postal 66281, São Paulo, SP, Cep 05315-970, Brazil
autor
  • Mathematisch Instituut, Universiteit Utrecht, Postbus 80.010, 3508 TA Utrecht, The Netherlands
  • Instituto de Matemática e Estatística, Universidade Federal de Goiás, Caixa Postal 131, Goiânia, GO, Cep 74001-970, Brazil
Bibliografia
  • [1] G. Darboux, Sur la forme des lignes de courbure dans le voisinage d'un ombilic, in: Leçons sur la théorie générale des surfaces, Vol. IV, Gauthier-Villars, Paris, 1896, 448-465.
  • [2] I. R. Porteous, Geometric Differentiation for the Intelligence of Curves and Surfaces, Cambridge Univ. Press, Cambridge, 1994.
  • [3] D. Siersma, Properties of conflict sets in the plane, this volume.
  • [4] J. Sotomayor and C. Gutiérrez, Structurally stable configurations of lines of principal curvature, Astérisque 98-99 (1982), 195-215.
  • [5] J. Sotomayor and C. Gutiérrez, Lines of Curvature and Umbilic Points on Surfaces. Text of Course delivered at the XVIII Brazilian Mathematics Colloquium, IMPA, Rio de Janeiro, 1991.
  • [6] M. Spivak, A Comprehensive Introduction to Differential Geometry, vols. 1, 3, Publish or Perish, Wilmington, 1979.
  • [7] J. B. Wilker, Equidistant sets and their connectivity properties, Proc. Amer. Math. Soc. 47 (1975), 446-452.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv50z1p277bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.