Principal normal spectral variations of space curves

• Petrovic, M. ^[1] ; Verstraelen, J. ^[2] ; Verstraelen, L. ^[3]
  1. [1] University of Kragujevac

     University of Kragujevac

     Opština Kragujevac, Serbia

     
  2. [2] Economische Hogeschool Sint-Aloysius.
  3. [3] Katholieke Universiteit Brussel.

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 19, Nº. 2, 2000, págs. 141-155
• Idioma: inglés
• DOI: 10.22199/S0716-09172000000200004
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• Resumen

  • In the present paper, we give a similar spectral variational theory for closed curves in the Euclidean 3–space E3, considering deformations in the direction of the principal normal vector field. Similarly as in the planar case, the closed Euclidean space curves satisfying the corresponding variational minimal principle are characterized by their curvature being a function of finite Chen type; their torsion remains completely free.

• Referencias bibliográficas
  • Citas [1] D. E. Blair, Classification of 3-type curves. Soochow J.Math., 21, pp. 145–158, (1995).
  • [2] B. Y. Chen, Total mean curvature and submanifolds of finite type. World Scientific. Singapore, (1984).
  • [3] B. Y.Chen, J.Deprez, F.Dillen, L.Verstraelen and L.Vrancken, Curves of finite type. Geometry and Topology of Submanifolds, II, World Scientific....
  • [4] B. Y. Chen, F.Dillen and L.Verstraelen, Finite type space curves. Soochow J.Math., 12, pp. 1–10, (1986).
  • [5] B. Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken, A variational minimal principle characterizes submanifolds of finite type CR Acad....
  • [6] B. Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken, Compact hypersurfaces determined by a spectral variational principle Kyushu Journal...
  • [7] J. Deprez, F. Dillen and L. Vrancken, Finite type curves on quadrics Chinese J. Math., 18, pp. 95–121, (1990).
  • [8] M. Petrovic, L. Verstraelen and L. Vrancken, 3–type curves on ellipsiods of revolution Preprint series, Dept. Math. Katholieke Univ. Leuven,...
  • [9] M. Petrovic, L. Verstraelen and L. Vrancken, 3–type curves on hyperboloids of revolution and on cones of revolution Publ. Inst. Math....
  • [10] P. D. Scofield, Curves of constant precession Amer. Math. Monthly 102 (6), pp. 531–537, (1995).