Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Delaunay surfaces expressed in terms of a Cartan moving frame

Warianty tytułu
Języki publikacji
Delaunay surfaces are investigated by using a moving frame approach. These surfaces correspond to surfaces of revolution in the Euclidean three-space. A set of basic one-forms is defined. Moving frame equations can be formulated and studied. Related differential equations which depend on variables relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case in which the mean curvature is constant, these functions can be expressed in terms of Jacobi elliptic functions.
Opis fizyczny
Bibliogr. 14 poz.
  • Department of Mathematics, University of Texas, Edinburg, TX 78540, USA
  • [1] P. Bracken and A. M. Grundland, On certain classes of solutions of the Weierstrass-Enneper system inducing constant mean curvature surfaces, J. Nonlinear Math. Phys. 6 (1999), no. 3, 294-313.
  • [2] P. Bracken and A. M. Grundland, Symmetry properties and explicit solutions of the generalized Weierstrass system, J. Math. Phys. 42 (2001), no. 3, 1250-1282.
  • [3] S. S. Chern, W. H. Chen and K. S. Lam, Lectures on Differential Geometry, World Scientific, Singapore, 1999.
  • [4] C. Delaunay, Sur la surface de revolution dont la courbure est constante, J. Math. Pures Appl. 6 (1841), 309-320.
  • [5] A. G. Greenhill, The Applications of Elliptic Functions, Dover, New York, 1959.
  • [6] J. Hass and R. Schlafly, Double bubbles minimize, Ann. of Math. (2) 151 (2000), no. 2, 459-515.
  • [7] K. Kenmotsu, Surfaces of revolution with prescribed mean curvature, Tohoku Math. J. (2) 32 (1980), no. 1, 147-153.
  • [8] K. Kenmotsu, Surfaces with Constant Mean Curvature, Transl. Math. Monogr. 221, American Mathematical Society, Providence, 2003.
  • [9] B. G. Konopelchenko and I. A. Taimanov, Constant mean curvature surfaces via an integrable dynamical system, J. Phys. A 29 (1996), no. 6, 1261-1265.
  • [10] A. Korn, Zwei Anwendungen der Methode der sukzessiven Annäherungen, Schwarz-Festschr. (1916), 215-219.
  • [11] J. Lichtenstein, Zur Theorie der konformen Abbildung, Bull. Internat. Acad. Sci. Crecivie CI. Sci. Math. Nat. Ser. A 1916 (1916), 192-217.
  • [12] I. M. Mladenov, Conformal immersions of Delaunay surfaces and their duals, in: Geometry, Integrability and Quantization, Softex, Sofia (2004), 158-168.
  • [13] N. Sultana, Explicit parametrization of Delaunay surfaces in space forms via loop group methods, Kobe J. Math. 22 (2005), no. 1-2, 71-107.
  • [14] T. J. Willmore, An Introduction to Differential Geometry, 2nd ed., Oxford University, Oxford, 1959.
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.